<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

yIpyIr<K_Tn^T^;N:L`^C:yIu@K\\PqkhpvF:CZ:N;xYqo[;_fiOf_CS;P:FZyYUCND<KB`KC`kMXkEXLSTlITLStLMTLMTLQtmTPmTP]x^b;Gb;GBLN\\LN\\::::FZOF]S>^V>^`>]Rn^pn^Zn^p^bpV_en`>_b>OboNb>_b>_B:::::ry;pB\\j:@N<VZ;N>?R>=r:]R:yIk<d:NZ=FZ;F:>::=b:AB;Eb;IR:=R:=:;Z::R:JBNZ;VZ<VZ>nZAF;=B;AR:F:]r:Cb>ERB]s>=TN=UV=V^]gB_c;=gJ_dVaC?eBv=Xn=iR?f^ACGAdb?HCecfatRgR>DJ;DJ;<J<LJ=DJ;Hj:<Z:>Z;F\\<N<=SF=TNaB;=UZ?cF]U^=gJ_tB=xF[YfaD?cSvyiplj;@Z<F\\=F\\:vAeiUAy?]D_ODOCUWuFBAY^IGdAHdShpAHPCHSMet]Swmr_ktTkB]UVQGdEAwFQU=AU>]vcK?:<MoIMU<UeAmFdKwlRWlr`mtTlR]TNIITAHtS::::Zwob_otTnr]V^IGdAHdShp@HpB@sOat[_t`ge[_o\\O`nfxRNyFXsfh`F<yRNmVWGVfVtNIfNUU=EeZoG]U@ee?=pM]tmKEmoqjkrdKWkchSU=Jw;::::PA:pK]TPeeK][I@o_otT:XB:HPoIMQ<UeA=oG]udKG=vdKWkb`sT=F@:p_WRSZI;ZOeROyFg;::vKShhAHPNgdA`dI]ooJjjRQjTPQFPaQ<pMZdxS:bHhFZHjoZa<:rFW;NiFPAU@:n][XZ]vCI^oi[kfZByqUo]pPdSP_L`ZPPw[?odXnbPjCqgZ`tQ?dc@^lHebPiDpj>H[f^tON^C`^<ok\\@oVabJA_dg[>OeMF_CNgGfb^WeJFchntTNsdv^\\Fr^vqROq@xhjntVob@okZhhFNuAAo;O`iNwAFdNPgD>kLveNYfPQsdNaB`_QXg[goN`td>cLfegpjphdK_t:OlGagtGuOOb\\`ZPXwGfboO[B`_PPwGfbOg]COZFOt`IbPXcSXetV^E@^BqpCQ`FFt@h_[_t\\>sm>d`WctGjNY`lp_F?pFgkW?bdI]tFjNA]MX^Y?dtnjH?nooZ]V^Y;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::RwS^h@neW`cV\\>Oj^yefPg?GgM^bnFk`hcJ>ooA\\KQf^gpNNwG^b=PdY?oo^\\dq]\\@bLhw>OoL_nC?c;Gog^cLhfCol>Gs^hcL>cCW\\lFunHj[>kFNm^NZZCk_HR;R>[eB;IPEb^=tL=v;ABLKw\\CCkOHrEDkchrEDjTnhlNgQn[Hn:YK;`VFaL;XV;tLK\\NOtRLeoDdn^XlbLwO=oT]RCpObLwd\\tn\\RC`ONQqO`TO<SLeXSPKIDTDdSG<LLaNSLKMmO^Em^IqOTpbUrZ<sllr;MmjPSSmjR=SmlRSTUehvfTJnHVODPLLVn<V:=P:<Rj:::ZbXZ:^Z=B;Z?>bZ@r;Bj=:BNGJ>TJ:\\:OBZ[KZ<M:@nZ<R;@J:EJJmZJ^;R?;BR<b:Zb<LJD\\[Z>]JGZ;N_G^bBF^;?oPXo_OkSa^LIoDGjrVuh>d`FlSp`d`dgXlKw^:_^THjJOfbp`<_kdFbBqkl@rgf]D_lA@o:__bPwQOdB?lL?gT@^ChrSnfK`gKOnkF_<``hvbuV`g@d:Uj[@]W=KN:<J::b?]FZCBQKBHgRZCEmmBaOTsarROFSEcTsW]QS@eEFMX?aGUSgfiFTohSuBMWWMIBOogOOVq?glaC=ebnOTtadg]x?gr\\;Hs]XooBhEerMdF=DSghe_rNacCUdF=DS]hECU@CUh[FRSVe]FSmh;aD=AFBQX@GBTQxDCU@AEKoBG=U_[CCCHTKHZ;MJ\\[ZB:::::::::::::::pk=<Nc@L[dPLLS<\\rO@OL<Th<t^LNCaPd`tglLbXLZHMM<X_HLJMOg@R]PKJLx\\lvZLLUMThdRH]vVTK<XsV<ks@lbTk>LlTQJ\\Dm:ETndRM\\R_aRKaPBLnbUrnHk\\@sOlNHaOEqpE<vXMkZXSQYnOpKo@]Sn`:NboYwp?^hieL`kQWglfwualm^uWapNAfLicpatkPvCgeU>u@`r<?j:B:@j?imsPU:ExQUoCqTGPOlUkulp_xi?>uQQqVgaax]`yovyaWYyIP`Hit\\PgHo\\RYwboaRX^FygsWpPGh_pgHg_AydtHwRakPvhvYsVov`xqg`dDYndgcwFkrvfpHZ;OwDxlt_caW`b\\:jTtOj<jBTQKevhuRk=YPDsBDSe`PfAoOXn^DYSpNGln_Un]lPghJgIl[TPJxtZPLCLQ?Veh^fSZ^_b^G]@fcKpfFP@Et^CUPAGEUG^EE]`L=UOb]t^\\rbAc:IZ::::::::::::::j<TJW<J]@R[LOG\\RBDn;EWg<t^<NC]OO<OM<TgDT<HSf@Sbpk=@OoPJFdtMDLAPN:]ofYKSXTStj\\\\NCeOmAN`uTJep>LlTeJK=Td=N?@rPHLcaNBLNtLLKaN\\`NjPr=DNwHn^`SP`JC<NKqN\\prD=L\\<SNDsbHMM<tB\\m>MNSAMS`PE<NbaUD@VEdVgDLliyDtNphXcXnK@qiqLkQvOMmVumiDwYyRJusnijf]MoTmdYpUtkBtXyqkmusYiJvTWGqNh\\UGiTwASsiya\\xTdnMawGaWQYKmEP_ivXYsPXQLiWpuXi\\NtyihNfWwroHaWOeo_p\\ymtn]dosYGboY^OV_ypgvOdlyewPyIxblqvG_uOphq_n^YwXnfiqxvq[tWviFkYQf@vZ=Nt:>Z:>:IBamydevamcYAYmMeUWSQMVcQYIIDmgYskcp_xdItBIvSgrUwRwiT?=wemDtAgx]Tsow`]cSwdtoxkYVpAvQoY`MFvWsgGeVsfR?Ixcgi]FSIXMmheMyLoXUmE@sevqEIuhnwxqGup_VomSKMe\\_YHggiOUOyqldtQ`xBqjqeJyYN]PXNam\\ho^`xqEm[EkRhWQtNlMMhmRvUMNiYA`Ne`mWhMg\\qnukOIKSTWldMEqoexPwHYQlRDuUExsBIXYmOXqxl]tMDvnTTX]uKujh`vg`VWAxMXKQmoHim^`xsQjt]MaxJJMklQpgLvUQWWaXDDwjYvFQXsXu`Dv[MrLqlB@Qahj;etrAYUTxmtqyhpDUvNQLNTv_PVS@peASPYwRdwW\\ov]yvuNEUPLWqGw^GHymoy?yx^WiC^e>pacf^Xwx<Oej@vnppDGejN\\oOvs`[;ApmfsTN[^Ng``gJ?tbhcKPaVfr;?t@FZcVhZVs^FbKH\\J`fSo`;_lCqZ?WL^[g@L^`_glj`^>Yd\\FZ:PZ;::::::::::::fJ[b==FJCB?Ccb>[[JE]TAMrC=oZ<NCaRO`R^ek:=W>`MBIQBhJH\\rVPsVAkN]TLHss@LPmo\\MTLiKFQUC<wTlPrdjvyr^DQUqngTL[lJwaJNdkDDU_`WSPm>qSZDs:ITZ\\pS@SjHtZPL;PX;do^PL;qs;<whLTN`NBHOJEs:qp=@nLDrPIjblL;TK>\\TC?];Ib\\FcD^nMH^EO^fvl``tYahROvAG__pfogv_@ma_b\\_ufnshQ\\>p^]hetfncFdcgwi@xvfy?QfOIobviohnkqaJ^xhvgLyhq`]Sgv[orVQ]Y_ZVhn;a^QX`XNujhoVikoXel`iofphyt;qimihjokpWd]WlA`p^wvwhgbwjUQl\\`x]ftgYyogoxp[pNwVqqcnaMQsIY_lv`Pac_iat^x?yq?Hx^ylKhwuhbUIyQNeYG`jpZABd<Z:BAYS`IccgsaSf]wUqWSeSW[yI:ayeMgaAfVqXBkgK]CasFWowcyr>Gc;OHvuvmyEQIUAsCdeeOktkMVkgXpYTZGxpWYW_SEIhiKtOYyY_WTuYdqUMqeSYx^UV_MRqOVnorxMxo[GsGikEyhiXGETcOGOOWvoCDYuZqF_mwKIwmsxCUv<[ugCTscrpmsWUsmoCqYWQaF_=sqWsq=suUfkkrwqSAcWiECPmhoAyZgEoEWLiGPWgyGdN?YNIgUoDSgIaqDVQxgKsgwDIuc;SDyMbLuYlGtLSVc=x_Uy?Qw_UEXyWRsrlcwi]uYcT]au_KxmWri_SuWYkMxPIhnQwLcEWcI?kt\\WVpuUL_t^YvF=WhsTcswWyx=;yDiRG=eqYUfChlMiYGc`mtIAHysruiVQas?uX^_VwmhsCUHUToOHOeDuAIKgegKwpsilOUDosLOfvmsy;b^OfaQgVMUdetOYf@ofamD`kUc]yEaW^qETKhWsVgETGOWIUFXieA=wqoebcFQ=gD_tTIHi_YXggfYSQieUEdTsUtAx_mftggwwXGowv_h]iDQIcreubEyeYr:MDMQf\\GUSqRSSS\\GsB=Gm;B:?bV;slmJlDM@hRM\\vSUN>DMPhSJdvl<Sl`OUPNGEM_]w>=mJmnBEJrtRMYsvlK@mWP`oWYolPlTpvnTppPPipveqoQUyN=kFPPWIp^PtpTWYqJGdVGqQCPwt@qlDJ;`Nd`qF\\OFqP[hYopne@XttJ_qUEMuT]yQM\\ehxfw[nxYGXJoieABrCwyPvFQyOTxq<wfmyf\\P<xpf\\uTiOCipZYsglRHpo^YW`Poh\\MGaV\\lsrIqAaR^PkXiwqlxCyiSV[oaGbkGTIOTxuVYUraEh_=F<IeRwHWiWGwtsAhpUdLUSnacTMHw_UguBQmDJ=RUKwT_V\\ETqQh:cHaESDMSK]xcmR>uxOaWOixTuidMT:idtkxAMuylR<YYptj^ymrMptiLm;[E?AeSqdlafOmyBWdMgdCCchiu`aTcwu??thCGcEXWoxmcRhCDJWxwsSTwy@YgbGF_cX_]tNYtbgsdQw\\KC>_RbQsgScRqxO_s@OdMOV\\yGRgULQT?QwfOfwgd;qthwwEQSOYUlAWWQHpkiwAiWqYTQT_abY?xSkt^wU_II@CIeOrigDjqyMsISyrd;UYIgy_sCMwQacQGvm?yl;D[aCfWIvEVkydAwbngx_=UcCexmcPgvesHbKf>=wDiYv[GoyEFohVEILggi;FuQwlerbqg\\eVZidt:AVwSu=ZwOcs=b_qdccCsAgTWgiUr@sHekXgghioX[MUjiCuWcT_Cv]StqHEAc^;WDgvtEvCKTLihkUs>agYiS_?UOCexESgoxa_eZ;EL_GocbdEiPEsOWTSWE=EgEOBJGgsUIZivhGsy;RggFrud[EESaVLmrOQGtuXgwti_UZ=V<WuhsUQesLsISITwSu=:Vmnq`yo\\TgZE_h;yl?NasonYG]UAqoXE_FvGU_aHtEXgoxi_eZ;CLUBaKXZCUEmghEt>yGESUCsT`CgyOxsOiFSy_GutQtPOfbOf=GVPsYjQv?KtPaVQsI>IdYGxaEX<IDoWhYeGYWxydyWym>qT\\DS>qTlaOXQugDSntsL]WttNw\\MWLujUYGTn]@oEDLZmlNYKKXTKhVbHoOQSnPC]woScEsdBWBSsblEihUUy_vYAiBKwskTies@YU`ebtoiSUideiNaxEUgJSVhoDEgT]CyVAfGgVLqTGsHtAyPQyQcU]KuhSt]gUjsDcyI:EHawhpWGCUYQibfOXgUe?QCSeFfCHlWFOsDrKwdAdM]V^SFR=wPCSeifjoRaSrgiCMqcN[E_CWcibKcwfgbhuTaMcdixxcb_KiAaFEiEQquf[dgQyQOr@ODacyKitOgRr]fnoc>sTQOrEWIPkvngeeMTdWgYQiFSy_ht_xopEoh<nJyrtmtILuys[QI@_DrGwosVPasemviItS[yY]FfOCOYwpoVoMbCqwnIsDgVuqtWWug=wV?WdMWNISCgdqwsBKgdAe_ayZmxCwIE]sf=W_iT;=X;CexGUeWWwqy^GdlENdLSNHWDiT\\dtnQVG]X[YX:MwXTnMlUjTq^xIAN@yKTKFuVYYpiXnm@yy@SWAtcljUmSOhQSQqwmtUYKO`mRXWIPOODux`kTqli`UTFo^NsMq^D`ft`_q_v[qgL_eLQf:xwxa\\b`xjaiuokfWwMwlwXgvQjJWoGwrYwlI`n_QsXiaUPiggcHQwOWhVW^bQauqnw^sF@aTApUhg=YrAhku_aHihV`iv_dOIwowfIOjYYrcyfDoqHnhYwdsQ`[oya?iCYjt`u[pZVpqDYcqYpSq]efxUGyMfjUXcaxgNwiQIgpwdqhpXtvasY?rtWFYwuB;E=WrS[D:;B:^\\iqbTitpNliafN`lOXiSF[=IoQn\\]?iMfkNo^nAqDQaYO_jh[nAb]idAgrVNw_Ou[aZ^xl_Vrsq[SwlgItVyp<ymPwqq@k@^oFXgs?\\cieDHhhqyAn`yv_\\GrCwbO_fnpnWahsY]PvgBNsDGlLxgAYjaP^eo`EiwZiud>ypwdRadTAwHHopqkHw^EQx?As?@wVQdFxeNftS>rVinFWoypiAWqdYrgq?IuHQSREXlaVhECDWHQqt\\ocOsYmWfOiHkctvmtoYekgrRqEr[tyloEepypuG@mTtqGuqkMxleKwxjaxPE<kTik@`L]alQ`QdXqrpthUUpuvOTTvaPhTJy<KEtUmlqA`LSqodYs<twLmXOXOHxLVtUoLqy=JdeQPpqCyKGLyqdWdmsoDvTmO`hWQeVsUpqIXTUTy]LYyn]mVeapS]mfXOkynrlWQHpi=WNIX\\`xLHoMarshTmHMKQOh@slUwgqSwXxwEloiVh`SomTgUopTVgQxDHNELRDqKNhWqdQP`lFAQdlvKlpJ]rCELt`M:=JZUlvASl`g<G\\^Ge`n^bGs@FbM`fS_cJ`fSKDivO<p^\\rbESh]Po\\uAImWqVmYPaTMvIWhyOgeqntOf\\seEmILmXyWYxVLAYVuthLOkqYmayvushxrOdlIHngmtNppYAS`pkFdXrtttqT]poXYtImwRxY:xlB]LuXOcDymXNmpU]UoiyPDLMVuP@uUoaUOpXiXLj@vsmkOTPdiYoXwPqk;XK`yoseowyWVaxUqXVhqqTyKpV[dJipQ>aujmw`XLEhTi]rkmqrhY^QYrqRgLoNiVidUgEuaUnxYWMmVo\\YXhpcXvGmokLLwpj;uleTlpansQO]xOFqX]uW`DOm=heifuW[eo_nFxmncfNwtx`sX_dYeTNyHphFOaqwf?FsDWcci^Vvht>wHGcLnsyAZ\\xvYylnXwfyqF^y@Qqep`SxokOpNioWweao\\`a`girVGgcqg?@qSYhq`^UQoXWrLqwpYvFF[s>xhOkxfhv^lOve;>]XO_CgxnWqfgwXnsFQoMieapmsQjTNhUywFXeu>yDQkC>yVvcRxy:VwxAsWx`wynYPuw_w_QrEIq?O]pXyKFa\\aeA@ao@wp^wKQhv@ouH]bingoobwdWgeKohiGuU_pYH[VhcX`sZ`u^Io:yq`AcPo\\aXuSW^\\PlV_kYO`xgZYx`fi`khbZnrEXagWsFYxcVtC`uUY`enycxa]vlrNbpOvgyndX_Yqy_nd`AvdqkNVp]xjMiaugpghtpwoWqeIFf<gq@Q]jqgQGpQ_tDAhlol>?avYcSxnunyUnqAOovitYXaLgkO`yIw^Gh]MOkiAgoY]Nh`ZgcwOmyVdvnsaNvAww]ftawi;yhBYvYgxXhoYhyEFxY?vkItDxgC`ijowCOgKWl?G\\wnhqFv=GsSft?gfCYtViww`_OHe_i^\\GcLamuGmhoa_WsXfwUwkSyfaHq`w\\x^^lwpFhZhO[vy\\>xqmg_oIvoAtHioxYnnqpcPlva_oIibaiuY[qAsdOrLgiLhkwvjTXpkWuLPl`AqXXmpOmX`u^XqVGea`iopp[WgnyxdnoIh_RvnTwlxqcgY_``ddnpd@yXnrPfv_@hfY`hhllplnwxUvgEgrYwZOhr@amhh^A_soyh[^t@YqAVsFgq>`h^XeyeZYYqiFfUi\\UgPIt^cxWowfSIvGHusrgGUWSYuKskgDqEmsapnpQ`qt\\iwDyK=xrLhOLioZyscPpoXuPxqVuKYEkcdn_HSTHpeQoAxmTUxnpqVDQxxrZxrrItgEML]YquTUQVIyMUdjFXOK`uN\\VtiMLLqgirhPUVhmAqyEuQxyrZHUyLKAdkYAQpYyYHUrYnIqwJITQdxidPYEU>IP_IXLIkC=yTxxiTYhIYiLVo`Wy`lvHLDdtTesmppUQuT@WdwcP>hrQnQAnhp_pOeVXeIGp]@urxn;alIggoPih^\\_pi=hnnpoeYrv^xqqdRHuGqcxnaci^kQyHgxYxx^Vv@ynKhmqPghO\\ay\\@OigOjlypIPhfqyUfhy?bQIpnhtupbqXyoodgpcfhetpwEggApbGi]cq_i^wiXuK`v^ivpocMogL_iUQvSY_qivKPhQwfkIcOimWwnKf`PQluyndvnpPttiaQVgUItPwquG`UYuifcOobE`rG`uEnpx@_jywAonMX_vGiXxm@GpKIvyUpmxF]VsEsewRO?yaAuG?iuUULMcVUiHmEpQbBCHgYgXwCwYtFeBk=iyQwKUySaw]aeeodx]xtcVgOSbMIUYXgQtdEuOsFXuRCSewCEYSHMOH=ex[YBXueFkhieVhYhhUSyGREWU=gHiAgjwh]qwf]EQeSLoiDgr`CF_iFGOYT=Hh=wVwXOadPyClGWuigSWe>Iq[XXMMWhhYUeTYeQxDoXtQXPsgAQGqx\\@y@qOAtm^ASfhmalsv`qHhVc@OPQX_eLPYyaDKxlnvHr:IYMTnO=s]yRNplapvy=jQ`P[EwcovY__XpqEwqoNeEidw>kSoyhib>qyMqixx^<PtxyqCxxofrLGt]akmxqlXd[Hwa_c\\awqwiQA_qY`bpwXfxKAxYpfeP_hhqBHxSXdsGmQng;gdPOdxattgeEY_lAqLwmPymsx]IOxvnrVYuw@]aPrVg^^AhRYplHniAtwi_pWu]QtbvpqnZ^Hqhx^jHpsgeqH]h`trWwjqhhNsUQygXnk`p^qtUqpxIonwiQ>vaou^NuSqefxhN@oHy]FIpDgvsphrhpdyf;gesvqmVcXip_Y^uwlLQhpqopV^I@[eQnOOhwgjEp\\]Qin_pYAijh^E?tmia?wkxGgLoncNop`ompoYIhlXqTVo]AslAlsXal^hd`iThaXVsLPxg_empanve=?auPuPWxhnbyVtYOaTnqXWmeIcqgrSxtdnsXxZIc?EgWeeUWrKUu==tfCWemcWgWXOXvcYauidctfMiScgEhq]]mHqpl\\usmTNEPdyO>yY:\\wAIOhxkXTqvlM^itutx\\DQcXSTALkXoGTocQsWXRVyqcYqq]VomXBIscDtpmMg\\xPYpMLwhUUdQtHxomdLfXyKtvPdqA@NTiwDiTiXY=pw`tRT\\yBMLwhp\\tob@XYiWp`ni<vREmrPPnDUM`s`YKZDmy=J;xqtLr;plLEptPouuN`hxctvqXqQaT[PVUMWW@QDITItOCmVx\\jkTvVIobLQx]mrXSsYmqTOqmo[eRSmSOAXOir@aLxuNuTmiimrPWCQWLuyeMvxYJ\\tyIIlCyoe`S=aor`UspWXilxpMSdoi`m^]yYmwwtrcQv[<q]EvylyOdqMyY:pxWyvbuk[yTsUyhlwMUquLTlO]qo_vGko_rsq\\I@mkyfwWxJvuk^]HXr;>Z=>:GRaIBdKF:ODdkS>XjO@QGItKuoLxNChWd@o_pRv<Qk]oD<j_IQqXUV\\TOQv\\@ocTyx]Tc<uqhoOYutdxrqyI=TnexkLw:xvCmVUQsNtmy=jgARNTXhdrxhnp@Oo@XpMXqdTA<JFT_gGx^hlOfeww]@inpXxf^uCGohn_VXc_A[EQmFwsvV_mvvYvd:f[CFodpobnfBGf@_t]Y_hGkm_cPAZO^cnpovOsBPs^^bN@kW`[:^rjNb@ibM`fB?[l^^Sq\\M_^Sn\\GGl_O`;Gl__k=``^Wj>Vo:Ylgnr@HoOQx;?q>OcV_=mfVocWUirIxuQxwmbWUfgAYhWgTMvWkvWSs[mV_qs\\eVTyBCEuwqwqSWvQGIufbYTeUuTaheiWWyd?ou=mVVcsDiu_uxYkgr=iQMIQSvhmFQUcmQinkwi_S>GIMofiUDKoFWYtNgHeUw;_GQeDMyTFyUmQuuwerUhhiiPOXYQwZQSxQfyquQquwwR]yWR;iwQxx]ts]WOWUKYCgYvQquIaR:OEacfugeJssQ_IIuE`Oi^uTuurhqvI_dPsVdCI]]tGYDcUYh]XUWEysFYsW`GiQeVtay_[xhWvoQHxWuGocn=yj=VSUfcexcituys>Qg\\MgDASOiH]iWpYhSyQcdLDQOvtkQXMyirIuQiHwQIRV]ogqPe<os`uYhq[UWsHqy\\xVYylqxTDxkmmWIoUiwIdQIpQiIs@YLoYvSawWQkneyIypy=j<aqwQrxQvoaU[AklQk^yQSpyUypsDsVQMquTiXlRToPXt[qUIXrodve@pcYs\\IKw@tVyqrXvhQPdhti<uniOiDys]mI@mywtwILSbIEcsmuy\\sYiXy]VGywbyvfqyy=jKtJYtQ]DM_HWKiyO]YExvtdvWEvsxtJALj\\ofHMeLxhEKW@ufqT]endtpHUxnhnrlp@qxgMnpYn\\lMsyPTiX<xwrhRmyNZQUmqy=ANOdLFtMllyGtoq\\WthWumsXXuwAk_ewJttq=tOAQ[]qUeLYaJxxMZIWSuqOhyMypMtkVTMhQLgYP@\\TXmYAhroPWWyVuYu^QxrEmh`sNIlcQx`logut`Dqr`tlylfTSXlwLpvHlVp\\raipWuPYMyeHlHuprMqxHTUqv^toWaPuUUAulMDx]yxKvvyAZ=yhBQxrxmEx[vxkQwmyAZGvu]fhyAZSwsawy:vbGyi=pr>ixRyu?x[^Fibnmux\\jIn^Yk]Pnuwswpi?^jm?fahjooaBypda_[NqG?e:imswsWqeMpnAaxmhs_x`twrSXv]^snIehVq>_i]iwv^xQW\\Lqf=ynopbinqaNmYhfIXnqhyNyy:nmanmkPipgfdxuyN_Up]mAmOa]riiOayF>dggdhVttppeOhDPiYH^DOeEYk;w`ggnin\\\\xp>qmOQiqGfav`QWdexy:ZQTmUV]sBXKY\\Qwy;R;yxhYSROyYMuvQWmkIIETcgT^oHqgwwqcTSy?yW?YIXYGs]EusyLUhAEhEcBHQideWBwViiiXiYSadk?dPmdtgGQWwiIRvCdrWIhys_yfNQBqiFnQhGsR[QUCMcHMcDkrbceYuf]qGdgWoYucYhysE=qw]uyWwEy@nSuQDtJ=@x]XstxtUILbmx_qYRXmOYYHpU_yY:xOjuRALyYayUmmeAUGTy\\xxaavFXuQiYQ`qQEPTlxAuwIEsShtqAucmwQ`xMmYriMDYlphY^aT^IUGtluXk:ixxxkVTqvpSqejFHsMqpI<wfprtXVqtuEiP;QySUmpaqihvV]MsutD]Xjqo=qPhMvYQKfItQ@ojyTQ@YlyvQuqO`tYdMHQU`QYV@kL]rLlwv\\s]aRoUmViLEILi]uHLqTljsiQ_muE=xnHwbhtl`TL`NTdQL@yZlmwlQn\\q?UWduL_pMcESwyntTP_`l`EY?iTXPkgeumalxTtimtryXmyjNmXVaVYuRuEVvqnvpKWIt:IuX<KDiufIwuxrddPjaYeiPMhPs`laiuKeJpiudqMxlJqaYaXyuTN;xOqhNvISkdrSeqvpuyHkaIxwXWKXSwdmWPyPYmk`QsdskUxYAS`iwhyp]Hv>qWaYRmAQLYs\\ykvdQAhNhdxXxLutmkyLA`S^iWseqUHOpuqoqMAHyCaYpplIdooIWnqxxmuaHl@elherxptHxKFIMetN[LrH@pp\\lQumcImxyqJqoeptEYRmlP>hmUAtILkipuPakCAybxqZTpbyp_dXYdYJ`Y?Mm^mrW=XYUr`uOFiX\\PwUqLUYuFqMIqXHXSwlnoEVaLXdYoolMqYWWpoMeqXtM;@odeqyljCXPKmucHl]QqxurYIkBIYUtnW=w\\YrOhpAuwEEYIhv:IqglsDalZMOkyoXmlOIUXay^auDhyhyiCgvgPmh?uCiwwX\\g@gfYoAvf`aahgjriskotrHy]p[YYiaHhqoa@ffhWhihgOFiDp[I@jeXkFabPhtPgtDHi\\OiNXfsYm\\ipqafeorTXqBVsvhsmQ`qiowGuWvxwynQtY[GsUYnehYQRiwfawysMfgEHt_vhqUfId^ayYaGIgWCwWcKxkeVPch_YXdexlcH]eTP]hDqFpQYQUvqav\\gEsYimidCQYDocgoUIIV?qhNmgEUe<GXpWunYwG?YW]uBUdQGtdYG;yX\\WxxwfkiFL[yqqdniegyWjcyfIvMqenoUAGWG]WtGEGgemwyugi`UD@yE\\ATJAg?cBhouaITZgUXUrjwydygYEdoiGMQwDSTCEtwiDvOCqiry;bDYyq]veAb<mcXsvp;IXMsOGen[UYUu_cTeubdSwDqR]qyoAEoeFXiINcI\\IyrUIFaWIeUUWwv?W^OidMuJ_EYui_gdgeDNsW\\?SV?S^kcbaGDoW:efMSvt=xNoWb;bl?wfOcocFumCPQyNgrvavViR>WDmcWlkgkuGg=GlCxjyWXqsfOwMsfuosXWdsWEO]UfeTtEcCcFWIskwHYYfIWwQMH]YWqeHCiFkmyEACWKysyuhsy>=HkqX?EhUUyogUU]HVOU?uSOqGVcG_=U?crh_Rb=iU=ydOrpitBQc^]eXAskUtXyXXYyHMtYChhsIX?FMGT?wvbis<QfZsUn_w>SVodX@emTawTMPwML:LJT<J:<JZ=N:<V:>::B@GF:eBm[G[OH\\OHC;DaKVaSB<;m<mt?U<=S^CUP=cF[VZgRM]fSSF^?ETav>Mc^SjtxY:dvjtNk]yLux]Dwg\\kd=WjmqZuSSuL]pvYEriIwQLXshWn`TnUYgEyYAVHlugtlt]vZUqSIWPik>HO[\\mweLaHyx\\VtMMQLuDAoXPvHUUfdTeQLFan^PNMxrS`ukuyiDLrloGQwITLwPV`EXxUvpaugAOvEwtDYpImVqqMxonTpQuklhoTdy`hwyhO?YMxPvy=jXxtXiyAymAQQgmsllWoUQy@p_QrdepduUTXyiYtBYrnTWttTXYMxiMV\\uiarIluA=PvhWsHWLlyblxppubxnXiKcuyCyrWyofILQXVveVNiOqLXp`thxSNdtHys]TsOMSvluieYQpqviQatU^qufaYHinSeXaHowqnYaOfawMTvrlXtXpEiNwaStqUgeyO<yKlUjAWyE`=@yyAZC`sAiqeNdLwknNisirDo_gfdnFiFVmwV]HX_QHfpgdPIuQqvagcPQutWaufyfhxrwl]hi@GhrvqkviQiykp]Ail\\Py>@y@oeMqamIlV^mcPcYN[^xdZhgphdGw[ggoMifM@xfFugHsXich^\\agnPofuy[Wvfpfy?XcmGhWgriAiFQgWxbbAcQOgC?_gfyghoa_gNp`t_kHpmffhXOlGHi]Vmmi^WVmNgvQ_wvrcqcnehGEyCoHxuVYgIysDUAykOiK_GwQVQoX]]we_tooWgWDYmdMMHxYguwFZayPSDqYUcwHdoeTuRgyWcwRIOiGqTvmspGw=GYROwAsRXkExwbVaS_oWcAhNaHCquJYhUkiTabtAxg?yQsWsgwawwiaSoUyWESyitt;xjMFx[wxKXwmDy[cUmiAqt=UFpYctIDcwhVAsTUrpoyoobJYgxGXkwsrGyi=Xs;s`su=AU\\OeMcHHguBIhj_egeYJ]xwqvRsgSETNsdYEGyWbXgiDKwZgWyYJSqnZhxd\\TgirVaQNAvslPsiWaYxviy>In<]TxtMYTlW`yUDuhtPaEosMpR=UqMPWPNrxxOTqfEVh`kLQQnaOgHwq@RPljmtQkqo?irXTJsat:yNoaRXlN^Hx[lnvTYSyRFEmKlKv\\oiLKIYTluRUeNTIrautaUplYPmaqWAQslqDxnmtPdmsetj[UvghuWxNdhk?=YUXNvlvAQjrdyE=yVhPfeTKyJexY:tPuiOLLWI@ukLuTqNLYsvLoQdoXEpoQuP`nNxLJEyEHyQLXymllQLhywA@od=vXmKphJcmqmux\\`qKETfqXY\\nsiW[TwnmvfIu?YPkuOnTybloBHXk\\xwlkvhpUaKYLwhxlnYlWyofALulvq@N[epNusahLG\\oUmkIXPFtUtiq;xsVIxOTyoewVEmpUT_XOnxVUqwnewPTYYyvV`lWIssXSE`YIYTmlYFtKatRQlrtisO@oSak_Dr^HUGdQTqsXmwl\\NouJAPyy=jlxvTlX]pUCmWHYt\\\\WAUqxPxBASsdxlaLW`QCHUVMPfLoUU]DylOWpaWn`wlmhedNmGo]p@]MYllnwUhlvX]hgrQXeLAvTQyy`smytq^euXkFooDomVfa@@c?isKIhaWcfgprQorVt?g`vppSIhZA_@yndPukilE`dQHai@iaAfgOyTFqqwm\\Oatpsthx\\GqfYxiyudYeHxlAGmFApkqguxgQhtxoZwXo_Nrgw^;Yx@gkHysPg`hAaXfxq@eth`TqkHwoOgnmWdKQwQ_uKodVieXftGYx>go<ivQabIX`agiBapb`xEisyGZYIy=P`nah@QcCfy?xrPihuWoV^]QnpvPxowpgQsRntXh]QXeL`y@WqQvhUpxXNeTYhco_[W]lWmiaggIfZ_hPHqvqe=a\\]hqlxp@wwkPgaxnHgsr>xcIb;ohPFaI>cnpmrybHQloffYO`EibUp\\vhvnQ]fYeLOmOYsnPviGqeX``>prA^nxbqYpIqwY>\\tgqlXmIGlPGuTnsw@shAuOh]uns`ntwqxuHtSQcHxnWGh<Hag_mVqmmo`=qry@_hfdf`iDXfSOsiXkf_wiq`NXvUVo\\aewnZWnqAQd\\iiEHk_ax]qfxf]XxpohaS?inihkiwnInRvxO^iCy]<ymtOlpQ]NQgbifsqkva^gHeAx\\TFqWvp@y^IvgqamfH[L_wv?wtga\\yx_A`Ofnkqun_xmwfUHrNHfxo[yO[L`gQqqhW[uN^j`yrf_jfyiQtsguyho]NtcXaU?xlFvSOwVIclqvHQw@ippIdHQuL`oSptwNedilKWvUqfhIuf^ieGcyhhk_dvnr?wnIphPwuOyfchpkY^Epquxgafyv_x_x_mvkrxoCnmIXghgevG]]@gw`dgyxkgbyX`vodx`wHpc?nwO@wqNsnpi@wy:>mlGnKpikvp?QbnvoEH`ugfgX]Oacq>]pxy:nrAHmcQos_cS?wsx\\\\Qi>PwoWtpamwNrxqrRGg?QyXqb<wvK`]Uw\\hVstHkrWmy@[]ibpvbFPcl`xXXlasCAu_QEI_XU]UugsPuhFUgdGtrIGb]yTww>ISoyXcUI\\QmeINGDQp=tfpSNuwnalMLMOEWXprhIWQdxciLCYTs@XpMMpEq@mUAMthMkkTLaitoHuAIj_yPqPueUll]yFXmIdYQqyvqk@eRhaTYpKNAXlmooqoHyvTYlQ`oxps]UL_MTMDWVDWvUuaUphyllhPdDw;]W]MvIAPaPow]mPUNlUsMQya@mXhWQdPAMxNAx[]wdhrpxwW]ksqprYpdPufEv]dSiQWctruYUliQ>@qdlL^LrdPk?DLulml<S\\HMv\\oIASlDnxYTutjBdqohWjIqmdNHyQFMKIMLL\\uL]\\t_kpYpivvRWqQnrKpkRHbromCHronnDOoNHgDhurXeTgg?ibyOc[hd[`bAFemw^TPupHeSGqUFyxOwG?gAp`_IuM_tp?lVX^tNgOOtoy_l>cEiglYsTOobxbQN^y^wQHmEvhaFGWR[iysYylIVTuVmieAEglsseGFWSeuMCvkWd?Y]]h`oFeuTNIIQ[Xr[VuoWkcWRQiaUVe]wwwB\\WRSuVn_UhQiKqyW=YWgT=as\\QWQuvteeUmFR;R@cC:<JZ=^:Yb:>Z:>:NfRbJCElSDdSfbCTLKXZaG:]S:=tV?SM]fS=d?Et^CeLCu\\?SM]VS=c?ELKdVlHRRpOgqthHSHisOAYW<JbPp]EvUqRrIL^DV:ERSLppUYsQPOIxtTM:XJUhmTLroQVCauTaoVuVXmMa<RC@kllsoiq\\\\rXlohhm`eXTLO\\<RJMNQHnNYKE\\xF=`VvsKagrOyGAerqhkitZfkZV[\\FnPpy?Vmvafrxx]@e<>]gfwPggt`ndQbugbSxp`fuYGkLQZ;gfVxqKagqWsPy]\\@uiylfPw:^j_>mffwpggwFcO?yHpyUQgvipGOqsYm:PnF?iuiifxhd`]vic]?Z;_\\^OfAQ^t^fb?ZHngxfth_roqti`rMYlC`]N`lUQnha`;@^lxuav_nYeWvwPyaKagrOyHAmBNbSojXytIxgHPmsQm]iZO^bbHk;@c]n_P_[lNmqW=QE:WrQKigqSsQy=]HUiuimDo[bZQXHQgS[WakuiMdbGY?mwjIWkIDj_h:CBaKYUgbBQYkmYaKReOC\\;EN=cLoR_krk[tJevVGugMcTQgvicjoH[csK?FESE\\KTeawaUccQXWQWwQFwQVAYQt\\PGhN>`sSdSUit?@uYaNKuwXhuiLJcPmnTK;=Y>iwlLoHhJtTJCaV?lOoLpXUUgiU]Msx\\XnaPIDSAtRLTU\\`y_\\X>lpRyOD`sgEWGlN[EyTpSXmVU<qpaWvYOIDypQLwQNLmwF]Lcek_LY=@RJHt^TrwpoNYUMFeOAtgNZ^OhFp\\jGn]GviNtVOvgf^FG]hXv@QxMi^NW_R?tlHo?VbP?lLa^NFwlvu;ijsQgUhhqFwPFllNasVod_pu`rpYoXw^HOj[H^PFeTpsn^gd`bphjNP[TNlJ^eFvpjg_Xqlcx`Mgf<FjlY\\=`[pWsKgh\\yrwnpNiuWgc:Ac@gnSh_gotghqDgorYmLNZ=Gnl^ZiNeQWn\\hcMArk`[:xvxIlagqAHwPViSItSF^PFeHiyXvsu_`UGrqhgcOkaHkb`f>h^VxwKawxxtea^pXgWZK^^BgbPXhPXs]gqtisr?uPFprIrkww`_jB?lS_^CPnBNm[Vc\\OeDPnSWdUPaZvlk>ZS^@;vTkv;gCwar`ayFOXnKhlMXhqrvOtM?YSQeHOixIXf]tkIUZUyN]hoefbIGU?xgQBcgVrWCoUfRSxsgTT[e>SWQid;aTxOyvADyCyQ=URmflIgKWXsguqMrXQXtoc?ioe\\mUPTvusyHYR@pdIrp=mtYtjYJ_txoTvaLOMySDhnbTxPLX_ywZelGpPqqRxdPYYnM`TQurtywexw=dpKaT;uwt`UsMQyTl<AqSHsOYnlLPwyL;PTSdNlDr^AmBEo[`T?<MB<v:\\R:`kFtJKQP\\PPSLNn\\O^iSRDn;ATJ<jGIKL\\VBAkCLLK<s?El^ASj>cl`gC`cKh\\C>oQIlW_yU@iVy]wXhlX_qal;GabVuHXqH@kIIyVygnxy:frRp_^Qc]itqvdSauvPk_^hdipsImEAseqymw]giy=^yPyayAZk`]c^ecFqywcShiy>kEAvtg`Kpfi_c`VmhibA`mUigWAsshotVbpxeeGyqW^Li^=wlXnZT@\\F>[;?Z:E:;@::Z<AjBnZZ>Z:gZ<N[:@d:>o:Nk:vZ:?nZ>jP@lLIZDn[>@wtF[?^hGf^NP[C>\\=?ccw^:Gn^FbGV^LAcb^^;g][^nJ@dBOjtVbCG^C@\\=KM^bJNtgf^:`^;oeKHwa>b>V_Li__Nn[HbP?jJYe:?nJXdZPeE>wdF[?N]B>qT>_gf^KpZwOZk_`cW\\BHl@nf?Xb=GjANZCA^`@jU_nEHk^g\\F`hO>Z;^t:GZdfklFZJW[dNaO`tcOjCQgSne[HoJNpTGk\\fp\\FgJ`nKa^?O`BGs\\@cLP^CXnffnk`^@C]acb;B:_CT=rV;BQ;HIwRWmgY?uryTTmVwUtVoSHyw]yCiSxsuwOAVsqgvkyFQw]cg^kgPKYKGXCGVLwDKouZOi;Cf@]RXIs:OY=sTB;GGWFK?So[e^kWN=dbMXFGT_eu_qtlsfIgRnMf>SdWWtOSttqXqGeiOsFEUi_HqmGvsctCu^[SweXagrtYW@uSQsGdYt^SdiiS^CyRGS]gdvWsKavSiscKXuyTVGQbtTCXoBXxpYXhlOnqVRtvaDX`LxtMuuhoCiMGPRNYx]tlXlRWaMG\\yK\\MTxPTpVgTrLEoLYKgun@@Q^`vNMK>MWD]RGDMWPR\\v\\kN\\^_cN`bC?[^P^\\Nbc>[Dhm^Akn@[mWpqv`IfxSicqgsiHfDYw?ohkaiUqvowwgqhiiaLogxhfpopRobTgpwV_Wxe=fnhWoZifcHXWcvuEdWwOWR_KXrsHxcd@[CQ]g\\wi@yEUWfteySkcSMeqIg=UevCTf[SsmVVGSyyHeqIysc\\WyPgtt_H]CwqQuGUUpQdA]VOSvaecEYDlEygOE\\sTxuVW]XlKIUmX]kFdETN?cleRpyw@OXfIipQfMMtcOX=cSxeb:AF:=DNKCF;BOOB=;R??rZPJZ<TZAJb\\<@JbQL^lq`XLmeJOPJ=<J;=T@P^`NZ:Nb^>tD`Z>>o<Aj>@gNv^^``j@[Ja`MPtN^^BX^;?tO@ZBCGOb>;BPeb:A>>jNO[FR?B;Aj<>]:N_?n:ORZ=DZ?Bb[DR]d:=BZ_VJ[RC;Db[BKIBJMC;OC=;j<DN[^D]XFcR?My>=VUERJ;Sb;x\\=fb?FT_GLaCH]fnMUVACb_GB?gZWCVACc;GdMBhOFZ?FdcDD;S<GXKOVKKc`=KDiRDlRneSmpNGHKPhrSTtf`kFTpBeTLdRjiVAlPo=R<Tj`<jeAm@HQ:Dyf]qSPsnaVu`vFuwDLVwhKdUWxevgXnRqoZAXUQtMPJkmwhLRilmeAPhqpDTu@UpjdXiXpD`wEAqEppuqkEEn@Hlf\\k[EXsdMpdoFPwr\\rHMuwMjCUKsLyR=WnMyE=QWAOPDTklVGHn^xuLAkO]N_TLP@V[`nGdURlQbuSThmGHNL<Mm\\O[QTr=RwEkAuLJdtVaRBitHXS]PlRUufqOLQX^iw=hJOxtFqVVqmDDOE@ygHXQ\\jR]ugAxDLvPMxV\\qJDV@YVYXl\\xKTirVAQu=wgMrgupXQvbDrTHP]qrv]kS=xhIOCaVBllBiORPQ:<J<xLkLPFmRD]r>]JLO>CbBF?kvgqcx?EeItt]uaivWCwqeBk;YswTeqx_qUgatxkuBwvkCxEabeeGmmY@AgRmuoyuEYE[idrQty;rU]IGWhOSwYQg>]cb=yD_WOAYyQsgYX^EEhwyMWBFYv<iFXMhwaHgIYQathKsrmHryhGqgBautKYdaxjqc@UYsWh>GWiYDuOxZSxhmyagUFSvRWDpiX\\?gqYxRwBkEWCgT_QeraeUUHdyuN?OREyOaNYDV=Eu;QnFeN\\YSG\\yuItVEph\\pNIlEispdOeHtgyNhiOUqWoXkEPQYHStDXa]T]QV[AucAWkIr[lMqTN`dyPQndTuvELbXqnqtMeKutt=xt<\\mlavkqV]]OrdQtiTZeQATod]U_qxppwtlseXJiuR]PxBumWAOmeW]PoV`QVLvcyuDPVaXNPAQChRxxrLhqOqr^dPLQSGHtXTKaDxRAmKaMOlWCAXB`xBxrVPJtXXQ@MU\\Xk@QXlsmaSCQYntQKmv_`m_DLClSgHtKPo_tXlatfyuUIRd]p@XjEqWSQtGpTuAwFpXyDPoyp_`NOdsZ]lGINmHQqdOPMTwTYNQM=tVAPwFEqUxuQ@QUySOTyGXm@UWVhtLuJSXTILxl@wlarLMpoySnMQd]MIYqylsKEqNTyrXNYpVpmrNqtOxspHjXpwspom`OremdPlPdojlKpiW]utRmlt]M_DoSak`@Yn<wkMXrHuJIsWTodQTfLTVIo@uNwXv`yP@ak`el]Um;iTutsOxmSPw^LmcXSCAYpau]xSYPOXhxVAs<qLadtHqS@aXqXodmvdPMgAsbEoPxODtVqHyg\\QTHnGTqHiVGuLcyrjaPblX[docXSslM;irbikBqYGqMMpktiqH`vuDkn=qoIWDxpDupbaRqIuvpoMXN?@WrDXutP_\\KeeyEek_Lvs]obXoSdtvUlfUqrqQlyWehSLILZutS]ph<lPQk`Ty^uwiaXOhOxtmnmNY=pWun@xq>uPUTjiupYlXEaTvTti`ypTuNULOqwETJmxOyEM[yY:\\v]hLyHWLpTrLokeTYDvYUwqEWQirwun?ewrYX]HX^Uxq@s@MuJQk\\DooaPXq_pn^PPcIQpyvy:Fnupuy`rbigu_jmP^oYtLwv=o]QipRiq[ockWoaWfYN\\XQ`_hp=WmlhiOW^\\`oqofEAbOPZ>``@Gj<_dD>Z@cJ::::::::J:en:=N><w>@J>Tn:ENZ`OBDN;ATWPJ<\\rJ@NE<o?QNCAN:PlZ<OLEl;<K;<J;@R><S:ELbms^\\RLilrTKCAV:LOkQN\\uU<eONDrHIlJQp;\\N<@OTLkH\\jbDT^=S^lS`HU^@W;DWNUKHmtt\\T:@jC=nTlVZ`U:EQStLcMxEirShu@=y]PNjUncLSMixe`VG@LoTKyMkB]x`ulAuMExPIuJh@Qq_lcovWg]wxqDpe]Pn]FamXcTGx^IsVV[egmSOf?apshbQ>[HycFqtc>iJFw?OhB_`\\fcK`g<n_bVj>xe[Wf^WecN[_ofINw\\Ho\\GrpAdJav;?sTag=AcEa_XovP_wDiaOp`sN\\?HoVgv;yhTHsh`sZwmAgamfbvhiVwfEAqViwUapep_fVrxogYw[>N`EAneykv_y?NiP?vnXuaaxRFwtvtSPaxnu??pWorQyZafxv?[;oqMac^nrZHm^ggJWs`WwPGk<qbfxhQ?wmfbTFhQiqbIaRwwLGwJffL@^[W]\\>`S>cV_rBobG?[C@^>N^\\NbcB\\[FdXS=`qgAsOauEpYyHwbmKp\\WtxTomxEyKkIqfEWyXn`ta@`geHh_NsjNkXOlUgbGxdhfevgxcoeBOoyAZwpnEWqE_xlOyCVbmWqDPmqhfHgqd`d]Hx@WdDgsmpdGgt^vgWqgbqpfpolwv^QhkIxXqb>W^oYfiyqVibVIqoWqQhe`Wyu@[HgyqYepNv[p[SqxCI]DigKXtXf\\KwotNyyphk@y]WsRiakpt?YsWPlQx[;gsCYqh_snncGo`r@hcPuJgjV`^[PsOPyHNqNWu`FhYqgTfe;grUi_uHqcOtcp]dhw?X_lgcj?glA]UYj>yg=WnxgbsYawYuPiubpxmiifhxXwqPOdIh]g^x]YkbqlVYwOH_h^dK`byAZSQmQhxTnpuX`kPg`ibBqqVw\\cWl?fxmX\\WgwA`fOiw`i\\T_hiHlWYsTYfOPhmfvDqqaV_nOq_a`xPsMaxX`nmYe@a_ghuqOdfhf?AylVglxcdIyQfgU_ev_sKxsBQk\\htnQmpauUYxBQeoIg]@vdyf@XxlW[E_iyhnT>hqxfl_vNhtwwt`HkNopDyai?sOprrodsAmmiyvQor_ntgn?V]ivj[_v]xaFifaPcP_eIxdQxh]HfDikLamKVmmyiBitNVdmaahiaGIaLxmponKGlAvlLXydWwbi[xheV_pQikAglh?eqOgdPlx_wHPlUhqaoqShs`flgf]pwkMOfNig??_dHdXVh`faV?s;yx\\pdx@fspZVpu^Xqr>]]aliiveVoUhlb_k_PkqX_NhgvhoXw]FvwhWmLhrDgttHqMWpjPvAAhCYm[YoI@m`ocPwgP_iMyxYGjfwhCyb<xnrYnKG[ZWwmI`lnudwu\\Va?XwqY^RvutaqKVnu^u>ajvw\\jhrrpgKgsL`hMibDo\\hIed>dF@_OQ\\]yu:atcxoVO^=WkqWso>v\\gxjamuGiAaspVknxhfFsKi`cxd=QmtVan^`]ab^qgpyigfhCAhF@ytYiHOeTyiGwqN^hRQmtYoIYj[fpDIqlVgXHmSNpooutPyv_vregEse=Sl_EbiG=mdRsdVMTtUgRiXReWSeFoCHwShhsGT?yRcWKSUxUvOiY]SUpeUOsrWQYnctVwEcqtRuuhqSf_T_?UxOwBUbPwsyLWgQqqdRyXRKYv;MrKXk`ukstqDupcxVgeQvtM`@ygQTyQUoAoMeV@eSvYSriKDDXYYlKewjYTIhJZiW[lSV`xSQKjuosdM?ArZJb>Zb`\\R>Zdf:;b<@>B::N;:;:ZD:B::F\\Z`mCgj>NlD^mB_pWGbrnlCgZnf\\E^eB?qTPl;ge:Vl>Oc;?[Z?Z>@@?DC?SZ[DW=bZEf:Af@=CK]FH;GK]f^gVJgB^=vFuf]KN:`VJQJ`Ajs<JQEquasHPnUXl^xMSdMa=ssHS]@To\\Leqll@rLdy<]tM]oT]RLTsVAKsdlsDLlep>PLQMNHPRFdvydjNMqrLLyYlZDVpmSYeRH`R[lvmavb\\QGQwWUQVUYv=SIGu`VdpylRVy<p`[vgF@qsAluhlSy[S_b`iv?IlJOhjibEor>qhjIoCFcCIx\\IrUgwK`igWtK`fgO]BqslFdMyoxFbsqiRQmOQqLNtaW^RGm]N]j__Dx_pgxCVbCO@[SC?rt]tb_RK[GQSdGUUB_W=gbFcS:[f:cd<?b?KF^Sf`[R\\KBbKF==B<KF^[d:GCMSiYegiyb>?Y]=FJmYAwbQUTnEWm[UVyugMG_weSuHWWxsWTQipwYW=XqsUmdiqiUUtmVkyw]quATqtqtopur`MkXW<ITOEuyTJNHVAxKpauCaoy=j^ho`qr]ITEtliXwQhw:EoUaPY\\KqyutdkJprEASqEvH\\muASMmY?dsQQlU^^OYmigdSYhwwrQg`xycLn`_pdTQg`hqyHgqHkieXYu`GupkIvKh]MfdAggewZaf]IhtOtSiVp]SECimWdrOwK=g[uhRWbdKrfqb<gxGQbTeFG[TeQh^Ec<ORqkGhMyc?r\\kdGUuLstBGtT;GN?bBcF?eHCOW\\Kv:sbgSXXoCh;sgiGpcwtkBcUhFuf<EGVMW>_W_IfRTWKQuChscdoiTl\\\\v>QtcDmexPEPwNeP<]p_ulgprdaNODsblPSUm_EV=xjcmlYdt?qppTUjPY]LMmPY;dPMLPRQpVYRqXy]MK_yY:`n]iiYIbJIs]PZTIpQ`t?wljBqGGdgh[oW;;rDigUgcokFvKT[SyTiUoWcD?gxEjS\\o[QukprTEnfew@Qv^dLKev<<JRpuQqkxMNVpPF=YwHtDLop<TbDJTHmaDj`avoLSopVtdJ:Pn\\PL\\LJNMK:\\RCdJ:Ln>`jb@Yh<O;DJd<J>@ROPJ:DL<\\TDJJ=J\\`Jb\\l:<KL<jBDJddJ:L>RC^Z:gl<>jKN:j<<JK>OJbDJJdn:CnKcL=FJnc^Nr:HbEGjQNZtqZLHsZNs\\ib]Xd;Xe;HomfZ<^_j?^KQnK>ZK>b@abZO\\=ObTF^CO\\CP\\KO`bOq>>s:GmGYm:?Z@fc:n_ZW[Rx:aywEisiDdOil]secR[GWIKxtyFjEy[CXsOICaFYafHwdtwBcaCxSbIISHoDhmiCkTfWeIceKUXJKW`_CrSVvAxQmd_GXmkgWoekCYJ_wLEE[sw<uBkmW?Ott?erExnYU`=U<EeNeeB;GsOeO_FC;GQSfrGU]CGiQT?og`cR<[tl]Wc_TcSe__FWOb>UTJud;?WP;TbCKGN_HGj:?[cGnrno]>nLQZ;>l^GuLFmJ^[bFZj>]B@g:G`<>[@>ZKFZ;HbJf]<>j<pZMh]<>jJFtXNvN?nba<GDQSHp=Utiu>oUhMUG[hrYyy;R=YGiUXOQd[Gemcr`=ShotVgdsEgUYt__DGKgviE<AEqgTcmRHwcPetTcI`wqcEW;yqD\\qv<oaUSQuqmpKeXSTHv?IX\\eWOmqFUqoHRQIuPhTaLycMrcHTcloxLnPtPBdUc=OGeTqpl]IrM=ql\\OxQVAqrnQlUxnvXqvmkWaoV\\kSpr?qT_xJ<yqBQkcxOBhwa<xt@muhjv`NVQonXXNUtwLSdXPOdmZ`Xxxu>evuxmLHsUPYlhsxuYciWEqWXYMixPiuqphsZak^espUpOqxL`KL`YU\\uB@uGiJs=q@MoEIpKTug]upQn^qt@hQXmM`xkDmsptYoXWVtvdLYYxQ\\=UWMLYuVLypMaL]uRUQWlDnGprMqKwXpKUUg\\qD@xh`o?DllaLfxty=JEhoSaXfHqs\\yodLw]RvMmVeMEPp?@ucHRPyontNM@xodLqlWOdsdDXs<QQtVaQLeuuS=o=uWldOEqjwYohXUq`LNducyrkLX`hqi<s_YtvqSPqT[UWPLWQXlqAQOMxf@sDiKGdlGUWtYva`r;EQ]aof<mTeOeDkn\\YFqli`uFhO\\euXih]wchvwZibNOtwQcfYtyAZ]XpuGh?XohprCPseOpdvqvpmxfhfpj[q\\NytrFsK?mYvYQEtyI:oxJQc]Ei=iVkWituIiGvDcY^aVy;EtwxmegTuUCOwVqIFetRIxmeW^ISUgtFydNOD]GIuWu_WgkyE\\qYxairqB_QuaMePkYyoxnYHxSBOAixSFaEexublkRcmgPUvy;rlogtWg`gy@WSMqt\\sVhEdGmuXgiuOhlKhWohUWtrmgjwvwYs>cSLgyPkCteIG]CsWi?]gUGTqCxtWSoKXnUVXyTgqrdQiDoiMgSt=EswThWdWUgkytMyBbetLGvPkcNWfaGUWsGGufluGQcw_OhrSfHYf^ot]]S^mSSmxtQX_ew<weaiHuoShiVcSsH[u[mRq]d\\QtlMvcKt]chliwY=wdYBVeW`edUMwkwfbqv`ewh_UNcfEGcyyrWyv_araGuMabGUSjqH[uYqWcaudaEsxIXygCIixy;B^ExM=x^IsAcRUmGh?ToWGg=IHOWtAGQuUckVxQVBcWbkCvcXgOSOkU@iuy;RxixqyDiqW@uxgUfdSy^OT<Gh\\cfPqEM?hkUtLkVCMFhotl_E]OCawEnmDqUcqsGu=TI]TeytSArZUulYU_QwtOVhIrtuIdUH@gbagCWUulsVbIXmGhiahUQva[hlawreiHqe_Uth]RNqwdSdiIxU=FSYuPagS_RggBrMic[SOIuG]sMWSyEx@WEs=eAsFTiX<aueabKExYutcMuvAfxmb_?wfmY_ysdwy\\UcUghuogJiRAurAqwlYX\\OumAFlsYgEse]hMwyvGrk]iqaiQgXKiTwMtNuVAyCjWgdodv=tGMRxaWbiEVegUuEDMgMQEa;edyt]muQWFcovrOTL]DaUVZEwD]w_?IVaYvoiMwWQey]OuWyBGkWXgY@_w[OVEsDemfagXsOUuYylOWdedesChoUMcGIewtiUVevdWxpAv\\iIcMyuoCoeIF_VheBH_iTKWPECnQgaSxWiu@[EhUYKOtVsDoAcP_rhufUuX_[FocwIWbCSBeqboWuLYc>sdtEyAYU`wdMAEmqXqMhDMdLMsn]FeaD\\my^GccwuKYt@gSHWR^CvreTdmcDICsIt?[mCamgdRo@oqILUQyJxrFlonHV_<QKQTXtvLXUPXmmxLGuSOeyiuX?`T_my;IubdyH]XqTkmqqkQvUPLgtUaUjGISeDXlIWtloEImaEpgPS@iWalomqkatv^tSBqVCqnZdTUuvqdXbYwcaXhYWuMqrUyCiuVEVdIt=`JoeSc`nLtOYHSHxqwYolyY:LUAQxNXNWLWJQu^PnbXqsQM?ySDasEyKVdMf`WeEut\\PQ]tsiRd@p>iS@\\U_UocMTv@QRlPqYmLeQtyswqOolUFlPCdnheVWAoe]xKdtc<y>XuIHKyTltluLYL<Dw=qm\\xNtPu\\EvSlsktvbxr;xrAaTkMPnhybxtBewfmWilLTTyeXoHi^_`_`vu?npmi_W_piYetWnOndQP`rFyj@snxw;gakvox^iHna>veMg^UaywV`Xo]@fo\\HdRWde`eovdNi]LO[GQmgqgpnWeFxMWTIfIedwGfIAI=GF_=EGEGOCwrWIv]YHkwIuYWYiugyBwTlqRiebCixLwhbIg@iHioCcyfrabUQbuWeG=YVoh\\cVsyr\\CtTATOQg\\SI?AiPecQIsBIc<gIIEy_MfDIWPOdIyxF=wgEEIqgDAIOeUT[xlOTCerG[Sm;dHEB=qB>WRZ;D;ABb[T:;BtcJZdm<<JBtj:gZ;?dOP:eBh[R__gxEr<CsZsReeFhqBaKdLmXc?UJOFZKU_?wgSEo_F<_R?KS;CR^PSKAqK`Lx`JBARO@yJev]MnR@jFlW@IKs`pLtVMeN^hpFqNPiru\\ugDsEyPWmoV=R]xp?ILc`vL@onPnJdJ?QTG=OnMR>eL?DMgmJ^DrHmJCERPdj><k[\\NtEs:PLE@S:]V<HJ:LJR<J:<ZR>Z:>`:?Z=>\\UX^MobC_[DXfbH^Z_[>_`Z>]:>^R>Z>w:;g:;GN=EJ=DNdm<<jDDj;=Tb>dEyl=xghfmTWyv@obQghgjQv_bhlIGjV>iSHvpXvUQmrXwcn_HOhNidQhk`_yOIsdatOh\\_NbmoqSieVnkcpaUA`]Aoc^yohqh^]TWlGOwOxeIF\\UWrqH]eOv^IqsNaTHv_Wp>__OPu@n^e>mjwqGOgn`vYWhHv`ZHvtFtqY]]ng>`tHogfqtbvvTQugPecwnifhOy^hn]]pbx^^kNv[Q[KUyWIIUHGOR>mhfOGcCe[Er`OeTQbLkWdOsIIUV?Tp]enaxuMyxoSqWR_?rZIcs]cQGTL;eP_fZMTkqTWOv\\=YNEYrqtlOtGQEKQYj[Xo;TbEC\\GDP=iJaS[OXlOX>]h@wWjwhjegX]Uhksx]YTMgEsU=cc<MRSCVRuggmTi]eqaf^qVuSFdYt@?bmacVgWiIimUTooFtcR@wCckfeSxWgytiSsch^OuYOeESf_wS=SgWEY;YiI_u^QWwoFdcb>oI>qWDKxkWFKuRhixLIyK=DQEX[QXQMrOEd>]IryDJ;g_ktFAiRAh?urHeunoTveE<?ejiRCeUOOHYEsO;Xn;DbgFBGhwqh=aHfaFNYUOaRuKRUgIrUYlmsYUgNsRMcf<SR`]cKSTewgoqdMEyTwBOcU?uiiwHKAwHWfP=Gv]iG[DDEC]]t`Qc>mRV[ThotCwd=Ev<MefevDgCdAikeErWX[?rZGc[MS`EuZOeWAiTOTfEFGixa=rM?BqYIEIfQ?WsGtT;GNQD>SFxkHfGhM[sesWwoch]yDIxpUwRsxWUUhOU_QuksWp;DbgVBmRF[UE?UhOTqQeEeUWErgoxOyI:askMwsAHhiHJ;g_\\kqqXUyl_aTLLWyMWITsZpXelOhtoMUoGupdtPHqRtejEXLmAM]lQH]OlHvMEQWiPiljDirB@u<tpDDwVQOdeu:En_\\xRExjhUUaoWYlM`ToHxL`KTxSJmSuiySLUPEOEIwPEl`MQ?ljIasRXNYhm`\\SsHQKMo^xV;qLvTkhPSkdNRyROtUMdEavvkrbECqQrOWeksydWGGEwA]edAFb[d^kdFSs<Ouy;bskUwsCxiU;sx@ieUG@JQArZlLBmRB=vTiJamYOTtvAWruQ;YTTIpVPYH\\QYMmQyjb<WJ=oVymRdRSHPjdo\\QwcqtLpvUDo?iuX`sNLqtiOshYS@XoeMddJ@NhkfeVfsuP]xQ_pog@o_YafMqx\\Xc`grLOhLAypyd;HtZ@d^WyRnoFpdpYuPgwD_ro?gYpa^f_gq`gVtEgmMnoW`iwvb<Gj;WlmA=URmWWmMXHusLaLDMPcuq;QoO=mSQk?dpBqo<MS?DkglLLdl<XJZ@T:\\TDpK;<R?@bJA_:>oN:::::FZW^^WNpTiZEN^FNtn`dgYmbw^<VoL^[t>gnFgOPpqP[TNl:?vmw`VX_SPiWvodhnCQokunsd;=Y@EWdcDmAx^]dDWB?_wFSsLQdVMtieeMeBwWboeDmKFwYcKicOoVvkIiMypYT;khWeXgwROwd^_rfMgNUtLYYKMbQCTkmI`Ac^]GeyeccrZWEFahMQu`ginuGqUDxiXaohcovnIc=uchqeLIY]mbO[wMWilyvK?st[cnEiLUgN_ubYIYKIRmxXGYBwgR;J:<::GBB;BR=CZ;B:;Z=>Z:>ZbWb:Vj^?]dabSIlNIgJ@][>o@nZG>k@>ZBnZZ^Z=>Z?>bZ@r;>dbN`LNm?_Zsh\\HOwC`ehypBinaX^CGiS`gQw_q>saXcKPopVc]`fVan`_^AY[@>mRGn[Hb\\^dj^wc_dhp`bYcC?^mf^;@db>`[fb:?NJ:N;;R??J:P:@::e:j::R?:@::e:j::R?:@::e:j::R?:@::e:j:BL;d<;FFH^:^d\\NvF?]@VgXPwbXv?y^ZYaPQqK@gaahl^oxi]DinSi^LWj]@b[xsSGmJ^yEOgXG`ng_HXvc_yd?dy_tyHj;no:xlLn`iYes@xCwa`Fe:GZhP^[x^FA_;N]?F[JocE@m;>b[x\\t_usOseNtDpu_?kmIqY>e?^tDF]XWvHpqw`iM@^qYcWNmY`lRoZJUZWIfSI[yXbye>YCWyeOcXiUc?=Rn;OmqM_IylaPwPPx]RXmxMeVBtoR=Jo=WNDQItnopX?uYculvDsmEQIAO[@jf=TbDxWaQSXXwtq=EnADKs\\YQqnyWhJn[gA_;_u>HiCy_pnkaFwKaiUqifWgggppIdZg]cof]yrW@syOleVi`P_yAZCy\\_qdZ?epvtbNn?Yk?>uZNldgyUW]lTxET]WeWyxjmriUyFQWFsT^?U]QB\\aFKISded^MgJaVAQd;CEgEUOCCZiC:=BmkH:;B:;:OG:KXh[dMCd@SEfErDuVkUeGoDbUDJaG;KcOQxBWU[MG=_FBOV]IRJ=f<;B:;B::::::::::::::::::JM\\RVIS:djHLT_Qt@YKfiPJ=o;`SX\\JYDvOtkpyu[iSilKaQt<LTSuZSw_WprvPlZ^wWaihYcPihWOph>uAv_likmalYhnEPxJfw\\ahWIpbG_HNi;qpuH[f@chVr`?jLAd_?ekie=@whXvH?lLuaCwhIvnEdxADLEb@ARJwE^_H<]Dbcs?MY=ES;or:JLLKnpjLdy[>lK_ntWcnpjKP^D^h@PlgY^La^JHd^``QHwGN^>_\\cQ]?Oq=Gc^Fb^D=qB:;B:;ZM>Z:>kJIZ:or:>b:>Z:::::::::::::::::::::BZ@J><JJ=N:\\J:>Z:::::XjyaG4:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCImUy0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIlNUtGKi0lKUNISUxEUkVORzYi

Vetores em Maple

No Maple, vetores s\303\243o extremamente necess\303\241rios nos c\303\241lculos e aparecem nos pacotes MultivariateCalculus, LinearAlgebra, VectorCalculus, e Physics. Dentro dos pacotes, os vetores t\303\252m propriedades diferentes que iremos comparar e contrastar neste artigo. Durante essas observa\303\247\303\265es, vamos considerar apenas os vetores suportados pelo Maple rtable, e n\303\243o o tipo mais antigo baseado na estrutura de dados table. Estes vetores mais antigos seriam familiares aos usu\303\241rios do agora obsoleto pacote linalg.

No pacote LinearAlgebra vetores s\303\243o essencialmente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-uplas. Se pensarmos em vetores como setas com comprimento e dire\303\247\303\243o, todas as setas emanam da origem de um espa\303\247o vetorial Euclidiano. Em ambos os pacotes VectorCalculus e Physics, os vetores s\303\243o setas que possuem comprimento e dire\303\247\303\243o, mas podem ser conectados a pontos arbitr\303\241rios em um espa\303\247o Euclidiano que s\303\243o referidos para coordenadas Cartesianas ou n\303\243o Cartesianas. O pacote LinearAlgebra suporta c\303\241lculos alg\303\251bricos b\303\241sicos com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=-uplas e matrizes, enquanto os outros dois pacotes suportam o c\303\241lculo diferencial e integral de vetores e campos vetoriais. Concomitante com uma maior flexibilidade nestes dois pacotes \303\251 uma crescente complexidade nas estruturas de dados, sintaxe, e nota\303\247\303\243o.

<Text-field style="Heading 1" layout="Heading 1">Construtores Obsoletos</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Vetores</Text-field>

O vetor original constru\303\255do no Maple, baseado na estrutura de dados da array, \303\251 inserido como

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJ3ZlY3RvckYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUZTNiYtRiM2Jy1GLDYlUSJ4RidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEieUYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmNvRjlGOUZjb0Y5

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJ2R0YoLUkndmVjdG9yR0YlNiM3JEkieEdGJkkieUdGJjcjPUYoNiM7IiIiIiIjRVxbbCNGOEYyRjlGMw==

Todos os vetores s\303\243o exibidos como vetores de linha, mas funcionam como vetores coluna. Sem uma distin\303\247\303\243o entre os vetores de linha e coluna, esta constru\303\247\303\243o trata necessariamente de vetores covariantes e contravariantes como equivalentes.

Tanto uma for\303\247a e uma fraqueza desses vetores originais \303\251 a avalia\303\247\303\243o de \303\272ltimo nome que as componentes n\303\243o s\303\243o exibidas ao se fazer refer\303\252ncia ao nome do vetor, como visto com

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==

SSJ2RzYi

O comando evalm avalia totalmente o vetor, como em

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSZldmFsbUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNj5RMCZBcHBseUZ1bmN0aW9uO0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lJWJvbGRHUSZmYWxzZUYnL0Y1RkYvJSp1bmRlcmxpbmVHRkYvJSpzdWJzY3JpcHRHRkYvJSxzdXBlcnNjcmlwdEdGRi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0ZGLyUrZXhlY3V0YWJsZUdGRi8lKXJlYWRvbmx5R0ZGLyUpY29tcG9zZWRHRkYvJSpjb252ZXJ0ZWRHRkYvJStpbXNlbGVjdGVkR0ZGLyUscGxhY2Vob2xkZXJHRkYvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRkYvRjhRJ25vcm1hbEYnLyUmZmVuY2VHRkYvJSpzZXBhcmF0b3JHRkYvJSlzdHJldGNoeUdGRi8lKnN5bW1ldHJpY0dGRi8lKGxhcmdlb3BHRkYvJS5tb3ZhYmxlbGltaXRzR0ZGLyUnYWNjZW50R0ZGLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGYHAtSShtZmVuY2VkR0YkNiQtRiw2JVEidkYnRjRGN0Zeb0ZWRl5vRitGVkZebw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSd2ZWN0b3JHRiU2IzckSSJ4R0YmSSJ5R0YmNyM9Rig2IzsiIiIiIiNFXFtsI0Y2RjBGN0Yx

Se o comando evalm \303\251 combinado com lprint, v\303\252-se o uso expl\303\255cito da estrutura de dados de array que est\303\241 por tr\303\241s desses vetores originais.

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

array( 1 .. 2, [( 1 ) = (x), ( 2 ) = (y) ] )

A estrutura de dados array n\303\243o \303\251 t\303\243o robusta como a mais recente estrutura de dados rtable sobre o qual o Maple agora constr\303\263i ambos Vectors e Matrices. As estruturas mais antigas s\303\243o, portanto, considerados obsoletas, ou seja, eles ainda existem no Maple, mas seu uso n\303\243o \303\251 r

<Text-field style="Heading 1" layout="Heading 1">Top Level</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Inicializa\303\247\303\265es</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==

JSFH

<Text-field style="Heading 2" layout="Heading 2">Vetores</Text-field>

Em "top-level", onde nenhum pacote adicional foi carregado, o Maple agora fornece o Vetor, constru\303\255do sobre a estrutura de dados rtable. Um Vetor \303\251 inserido com a sintaxe

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLUknUlRBQkxFR0YoNiUiKjtrKysqLUknTUFUUklYR0YoNiM3JDcjSSJ4R0YoNyNJInlHRigmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRjo2Iy9JJCVpZEdGKEYx

ou equivalentemente, com a sintaxe

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUYjNictSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiLEYnL0Y4USdub3JtYWxGJy9JK21zZW1hbnRpY3NHRiRRJDwsPkYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYxNiVRInlGJ0Y0RjcvJStleGVjdXRhYmxlR0ZFRj5GPkZALyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0ZARmVuRj4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqO3ErKyotSSdNQVRSSVhHRig2IzckNyNJInhHRig3I0kieUdGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GODYjL0kkJWlkR0YoRi8=

Observe o padr\303\243o para um vetor coluna, como pode ser visto com

Vector[column](2, {1 = x, 2 = y}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

Um vetor linha pode ser constru\303\255do com a sintaxe

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJXR0YoLUknUlRBQkxFR0YoNiUiKmNzKysqLUknVkVDVE9SR0YoNiM3JEkidUdGKEkidkdGKCZJJ1ZlY3RvckdGJTYjSSRyb3dHRig3Iy1GODYjL0kkJWlkR0YoRjE=

e sua distin\303\247\303\243o inerente de um vetor coluna vista com

Vector[row](2, {1 = u, 2 = v}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

Usando o ponto para multiplica\303\247\303\243o n\303\243o comutativa, vemos que o Maple respeita tanto os produtos interno e externo.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJXRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJm1pZGRvdDtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGUS1GLDYlUSJWRidGNEY3LyUrZXhlY3V0YWJsZUdGQkY+RitGV0Y+ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJWRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJm1pZGRvdDtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGUS1GLDYlUSJXRidGNEY3LyUrZXhlY3V0YWJsZUdGQkY+RitGV0Y+

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqVypvKioqKS1JJ01BVFJJWEdGKDYjNyQ3JComSSJ4R0YoIiIiSSJ1R0YoRjcqJkY2RjdJInZHRihGNzckKiZJInlHRihGN0Y4RjcqJkY9RjdGOkY3SSdNYXRyaXhHRiU3Iy1GPzYjL0kkJWlkR0YoRi8=

<Text-field style="Heading 1" layout="Heading 1">O Pacote MultivariateCalculus</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Inicializa\303\247\303\265es</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGTC8lJmRlcHRoR0ZVLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZRNiZGU0ZWRlgvRmVuUSVhdXRvRictRiw2JVEld2l0aEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRKFN0dWRlbnRGJ0YvRjItRl9vNiYtRiM2JC1GLDYlUTVNdWx0aXZhcmlhdGVDYWxjdWx1c0YnRi9GMkY5RjkvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGOUY5RjUvJStleGVjdXRhYmxlR0Y9Rjk=

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

<Text-field style="Heading 2" layout="Heading 2">Vetores</Text-field>

No curr\303\255culo padr\303\243o de faculdade, os vetores s\303\243o provavelmente encontrados primeiro em um curso de c\303\241lculo de m\303\272ltiplas vari\303\241veis. Uma forma onde tais vetores ir\303\243o surgir \303\251 atrav\303\251s do operador gradiente. Por isso, temos

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLUknUlRBQkxFR0YoNiUiKlcyKCoqKiktSSdNQVRSSVhHRig2IzckNyMsJComIiIjIiIiSSJ4R0YoRjpGOjcjLCQqJkY5RjpJInlHRihGOkY6JkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZANiMvSSQlaWRHRihGMQ==

Esse vetor \303\251 apenas um Vetor "top-level", como vemos com

Vector[column](2, {1 = 2*x, 2 = 2*y}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

Outra apari\303\247\303\243o do vetor no curso de c\303\241lculo multivariado est\303\241 em conjunto com a derivada direcional. O pacote Student[MultiariateCalculus] cont\303\251m o comando DirectionalDerivative, cuja sintaxe \303\251 mostrada abaixo.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUTZEaXJlY3Rpb25hbERlcml2YXRpdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDY+UTAmQXBwbHlGdW5jdGlvbjtGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvJSVib2xkR1EmZmFsc2VGJy9GNUZGLyUqdW5kZXJsaW5lR0ZGLyUqc3Vic2NyaXB0R0ZGLyUsc3VwZXJzY3JpcHRHRkYvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGRi8lK2V4ZWN1dGFibGVHRkYvJSlyZWFkb25seUdGRi8lKWNvbXBvc2VkR0ZGLyUqY29udmVydGVkR0ZGLyUraW1zZWxlY3RlZEdGRi8lLHBsYWNlaG9sZGVyR0ZGLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0ZGL0Y4USdub3JtYWxGJy8lJmZlbmNlR0ZGLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmBwLUkobWZlbmNlZEdGJDYkLUYjNipGKy1GIzYnLUklbXN1cEdGJDYlLUYsNiVRInhGJ0Y0RjctSSNtbkdGJDYkUSIyRidGXm8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY7Ni1RJyZwbHVzO0YnRl5vRmBvRmJvRmRvRmZvRmhvRmpvRlxwL0ZfcFEsMC4yMjIyMjIyZW1GJy9GYnBGW3ItRltxNiUtRiw2JVEieUYnRjRGN0ZgcUZkcUZWRl5vLUY7Ni1RIixGJ0Zeb0Zgby9GY29GNkZkb0Zmb0Zob0Zqb0ZccEZecC9GYnBRLDAuMzMzMzMzM2VtRictRiM2Jy1GZHA2Ji1GIzYnRl1xRmJyRl9yRlZGXm9GXm8vJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0YnLUY7Ni1RKSZlcXVhbHM7RidGXm9GYG9GYm9GZG9GZm9GaG9Gam9GXHAvRl9wUSwwLjI3Nzc3NzhlbUYnL0ZicEZocy1GZHA2Ji1GIzYnLUYsNiVRInVGJ0Y0RjdGYnItRiw2JVEidkYnRjRGN0ZWRl5vRl5vRl5zRmFzRlZGXm9GYnItRmRwNiYtRiM2Jy1GLDYlUSJhRidGNEY3RmJyLUYsNiVRImJGJ0Y0RjdGVkZeb0Zeb0Zec0Zhc0ZWRl5vRl5vRlZGXm9GK0ZWRl5v

LCYqKiIiIyIiIkkidUc2IkYlKSwmKiQpSSJhR0YnRiRGJUYlKiQpSSJiR0YnRiRGJUYlI0YlRiQhIiJGLEYlRiUqKkYkRiVJInZHRidGJUYoRjFGL0YlRiU=

Observe o uso da lista, tanto para o ponto de avalia\303\247\303\243o e o vetor dire\303\247\303\243o. Assim, a lista LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtaUdGJDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ2RidGNEY3Rj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y+ \303\251 usada para o ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ2RidGNEY3Rj5GPkY+ e a lista LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJiRidGNEY3Rj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y+ \303\251 usada para o vetor 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, uma fonte potencial de confus\303\243o, tanto aqui e nos pacotes VectorCalculus.

<Text-field style="Heading 1" layout="Heading 1">Os Pacotes LinearAlgebra </Text-field>

<Text-field style="Heading 2" layout="Heading 2">Inicializa\303\247\303\265es</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA=

N2lySSMmeEc2IkkkQWRkRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkSShBZGpvaW50R0YkSTNCYWNrd2FyZFN1YnN0aXR1dGVHRiRJK0JhbmRNYXRyaXhHRiRJJkJhc2lzR0YkSS1CZXpvdXRNYXRyaXhHRiRJL0JpZGlhZ29uYWxGb3JtR0YkSS1CaWxpbmVhckZvcm1HRiRJJUNBUkVHRiRJNUNoYXJhY3RlcmlzdGljTWF0cml4R0YkSTlDaGFyYWN0ZXJpc3RpY1BvbHlub21pYWxHRiRJJ0NvbHVtbkdGJEkwQ29sdW1uRGltZW5zaW9uR0YkSTBDb2x1bW5PcGVyYXRpb25HRiRJLENvbHVtblNwYWNlR0YkSTBDb21wYW5pb25NYXRyaXhHRiRJMENvbmRpdGlvbk51bWJlckdGJEkvQ29uc3RhbnRNYXRyaXhHRiRJL0NvbnN0YW50VmVjdG9yR0YkSSVDb3B5R0YkSTJDcmVhdGVQZXJtdXRhdGlvbkdGJEktQ3Jvc3NQcm9kdWN0R0YkSSVEQVJFR0YkSS1EZWxldGVDb2x1bW5HRiRJKkRlbGV0ZVJvd0dGJEksRGV0ZXJtaW5hbnRHRiRJKURpYWdvbmFsR0YkSS9EaWFnb25hbE1hdHJpeEdGJEkqRGltZW5zaW9uR0YkSStEaW1lbnNpb25zR0YkSStEb3RQcm9kdWN0R0YkSTZFaWdlbkNvbmRpdGlvbk51bWJlcnNHRiRJLEVpZ2VudmFsdWVzR0YkSS1FaWdlbnZlY3RvcnNHRiRJJkVxdWFsR0YkSTJGb3J3YXJkU3Vic3RpdHV0ZUdGJEkuRnJvYmVuaXVzRm9ybUdGJEk0R2F1c3NpYW5FbGltaW5hdGlvbkdGJEkyR2VuZXJhdGVFcXVhdGlvbnNHRiRJL0dlbmVyYXRlTWF0cml4R0YkSShHZW5lcmljR0YkSTJHZXRSZXN1bHREYXRhVHlwZUdGJEkvR2V0UmVzdWx0U2hhcGVHRiRJNUdpdmVuc1JvdGF0aW9uTWF0cml4R0YkSSxHcmFtU2NobWlkdEdGJEktSGFua2VsTWF0cml4R0YkSSxIZXJtaXRlRm9ybUdGJEkzSGVybWl0aWFuVHJhbnNwb3NlR0YkSS9IZXNzZW5iZXJnRm9ybUdGJEkuSGlsYmVydE1hdHJpeEdGJEkySG91c2Vob2xkZXJNYXRyaXhHRiRJL0lkZW50aXR5TWF0cml4R0YkSTJJbnRlcnNlY3Rpb25CYXNpc0dGJEkrSXNEZWZpbml0ZUdGJEktSXNPcnRob2dvbmFsR0YkSSpJc1NpbWlsYXJHRiRJKklzVW5pdGFyeUdGJEkySm9yZGFuQmxvY2tNYXRyaXhHRiRJK0pvcmRhbkZvcm1HRiRJMUtyb25lY2tlclByb2R1Y3RHRiRJKExBX01haW5HRiRJMExVRGVjb21wb3NpdGlvbkdGJEktTGVhc3RTcXVhcmVzR0YkSSxMaW5lYXJTb2x2ZUdGJEkuTHlhcHVub3ZTb2x2ZUdGJEkkTWFwR0YkSSVNYXAyR0YkSSpNYXRyaXhBZGRHRiRJMk1hdHJpeEV4cG9uZW50aWFsR0YkSS9NYXRyaXhGdW5jdGlvbkdGJEkuTWF0cml4SW52ZXJzZUdGJEk1TWF0cml4TWF0cml4TXVsdGlwbHlHRiRJK01hdHJpeE5vcm1HRiRJLE1hdHJpeFBvd2VyR0YkSTVNYXRyaXhTY2FsYXJNdWx0aXBseUdGJEk1TWF0cml4VmVjdG9yTXVsdGlwbHlHRiRJMk1pbmltYWxQb2x5bm9taWFsR0YkSSZNaW5vckdGJEkoTW9kdWxhckdGJEkpTXVsdGlwbHlHRiZJLE5vVXNlclZhbHVlR0YkSSVOb3JtR0YmSSpOb3JtYWxpemVHRiRJKk51bGxTcGFjZUdGJEkzT3V0ZXJQcm9kdWN0TWF0cml4R0YkSSpQZXJtYW5lbnRHRiRJJlBpdm90R0YkSSpQb3BvdkZvcm1HRiRJMFFSRGVjb21wb3NpdGlvbkdGJEktUmFuZG9tTWF0cml4R0YkSS1SYW5kb21WZWN0b3JHRiRJJVJhbmtHRiRJNlJhdGlvbmFsQ2Fub25pY2FsRm9ybUdGJEk2UmVkdWNlZFJvd0VjaGVsb25Gb3JtR0YkSSRSb3dHRiRJLVJvd0RpbWVuc2lvbkdGJEktUm93T3BlcmF0aW9uR0YkSSlSb3dTcGFjZUdGJEktU2NhbGFyTWF0cml4R0YkSS9TY2FsYXJNdWx0aXBseUdGJEktU2NhbGFyVmVjdG9yR0YkSSpTY2h1ckZvcm1HRiRJL1Npbmd1bGFyVmFsdWVzR0YkSSpTbWl0aEZvcm1HRiRJOFN0cm9uZ2x5Q29ubmVjdGVkQmxvY2tzR0YkSSpTdWJNYXRyaXhHRiRJKlN1YlZlY3RvckdGJEkpU3VtQmFzaXNHRiRJMFN5bHZlc3Rlck1hdHJpeEdGJEkvU3lsdmVzdGVyU29sdmVHRiRJL1RvZXBsaXR6TWF0cml4R0YkSSZUcmFjZUdGJkkqVHJhbnNwb3NlR0YkSTBUcmlkaWFnb25hbEZvcm1HRiRJK1VuaXRWZWN0b3JHRiRJMlZhbmRlcm1vbmRlTWF0cml4R0YkSSpWZWN0b3JBZGRHRiRJLFZlY3RvckFuZ2xlR0YkSTVWZWN0b3JNYXRyaXhNdWx0aXBseUdGJEkrVmVjdG9yTm9ybUdGJEk1VmVjdG9yU2NhbGFyTXVsdGlwbHlHRiRJK1plcm9NYXRyaXhHRiRJK1plcm9WZWN0b3JHRiRJJFppcEdGJA==

<Text-field style="Heading 2" layout="Heading 2">Vetores</Text-field>

Os pacotes LinearAlgebra e Student[LinearAlgebra] usam o Vetor "top-level". N\303\243o h\303\241 construtores especiais de vetores em qualquer um destes dois pacotes. Quanto ao top level, o vetor pode ser constru\303\255do quer como

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLUknUlRBQkxFR0YoNiUiKi9EKSoqKiktSSdNQVRSSVhHRig2IzckNyNJInhHRig3I0kieUdGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GOjYjL0kkJWlkR0YoRjE=

ou como

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqL0opKioqKS1JJ01BVFJJWEdGKDYjNyQ3I0kieEdGKDcjSSJ5R0YoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY4NiMvSSQlaWRHRihGLw==

Que V \303\251 um vetor coluna que pode ser visto com

Vector[column](2, {1 = x, 2 = y}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

ou com

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWdEdGKC1JJ1JUQUJMRUdGKDYlIiprTSkqKiopLUknVkVDVE9SR0YoNiM3JEkieEdGKEkieUdGKCZJJ1ZlY3RvckdGJTYjSSRyb3dHRig3Iy1GODYjL0kkJWlkR0YoRjE=

Vector[row](2, {1 = x, 2 = y}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

Estes dois pacotes tamb\303\251m distinguem entre o Vetor coluna (linha) e a Matriz com uma \303\272nica coluna (ou linha). Assim, a matriz

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiKlMhXHkqKS1JJ01BVFJJWEdGKDYjNyQ3I0kieEdGKDcjSSJ5R0YoSSdNYXRyaXhHRiU3Iy1GOjYjL0kkJWlkR0YoRjE=

Matrix(2, 1, {(1, 1) = x, (2, 1) = y}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoLUknUlRBQkxFR0YoNiUiKi9WKSoqKiktSSdNQVRSSVhHRig2IzckNyQiIiIiIiM3JCIiJCIiJUknTWF0cml4R0YlNyMtRjw2Iy9JJCVpZEdGKEYx

\303\251 um vetor coluna, como vemos em

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJDR0YoLUknUlRBQkxFR0YoNiUiKiV5JSkqKiopLUknTUFUUklYR0YoNiM3JDcjIiIiNyMiIiQmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRjo2Iy9JJCVpZEdGKEYx

Vector[column](2, {1 = 1, 2 = 3}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

Similarmente, com a linha

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYlUSJSRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1GLDYlUSRSb3dGJ0Y0RjctRjs2PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdGQi9GNUZCLyUqdW5kZXJsaW5lR0ZCLyUqc3Vic2NyaXB0R0ZCLyUsc3VwZXJzY3JpcHRHRkIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGQi8lK2V4ZWN1dGFibGVHRkIvJSlyZWFkb25seUdGQi8lKWNvbXBvc2VkR0ZCLyUqY29udmVydGVkR0ZCLyUraW1zZWxlY3RlZEdGQi8lLHBsYWNlaG9sZGVyR0ZCLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0ZCRj5GQEZDRkVGR0ZJRktGTS9GUFEmMC4wZW1GJy9GU0ZqcC1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRIkFGJ0Y0RjctRjs2LVEiLEYnRj5GQC9GREY2RkVGR0ZJRktGTUZpcC9GU1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjFGJ0Y+RltwRj5GPkZbcEY+RitGW3BGPg== 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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLUknUlRBQkxFR0YoNiUiKlMxZz0qLUknVkVDVE9SR0YoNiM3JCIiIiIiIyZJJ1ZlY3RvckdGJTYjSSRyb3dHRig3Iy1GODYjL0kkJWlkR0YoRjE=

Vector[row](2, {1 = 1, 2 = 2}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

<Text-field style="Heading 1" layout="Heading 1">Os Pacotes VectorCalculus </Text-field>

<Text-field style="Heading 2" layout="Heading 2">Inicializa\303\247\303\265es</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GLDYlUS9WZWN0b3JDYWxjdWx1c0YnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSI6RidGOy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGQ0Y7 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GLDYlUSZwbG90c0YnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSI6RidGOy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGQ0Y7

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEqaW50ZXJmYWNlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEsdHlwZXNldHRpbmdGJ0YvRjItSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtRiw2JVEpZXh0ZW5kZWRGJ0YvRjJGQUZBLUY+Ni1RIjpGJ0ZBRkNGRkZIRkpGTEZORlBGUkZVLUY+Ni1RIn5GJ0ZBRkNGRkZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZGW28tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGW28vJSZkZXB0aEdGYm8vJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRl5vNiZGYG9GY29GZW8vRmhvUSVhdXRvRidGZ24tRiw2JVEsVHlwZXNldHRpbmdGJ0YvRjItRjY2Ji1GIzYkLUYsNiVRKVNldHRpbmdzRidGL0YyRkFGQS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GNjYkLUYjNigtRiw2JVEndXNlZG90RidGL0YyLUY+Ni1RIixGJ0ZBRkMvRkdGMUZIRkpGTEZORlBGam4vRlZRLDAuMzMzMzMzM2VtRictRiw2JVEkZG90RidGL0YyRj0tRiw2JVEidEYnRi9GMkZBRkFGWi1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHRkVGQQ==

<Text-field style="Heading 2" layout="Heading 2">Vetores</Text-field>

Os pacotes VectorCalculus suporta as estruturas de dados apresentados na Tabela 1.

Vetor livre

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLUknUlRBQkxFR0YoNiUiKkMlcCoqKiktSSdNQVRSSVhHRig2JDckNyNJInhHRig3I0kieUdGKDckUSJ4RihRInlGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GPTYjL0kkJWlkR0YoRjE=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqLypwKioqKS1JJ01BVFJJWEdGKDYkNyQ3I0kieEdGKDcjSSJ5R0YoNyRRInhGKFEieUYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY7NiMvSSQlaWRHRihGLw==

Vetor Posi\303\247\303\243o

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLUknUlRBQkxFR0YoNiUiKlcsKCoqKiktSSdNQVRSSVhHRig2IzckNyNJImFHRig3I0kiYkdGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GOjYjL0kkJWlkR0YoRjE=

Vetor Raiz

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJVR0YoLUknUlRBQkxFR0YoNiUiKlcyKCoqKiktSSdNQVRSSVhHRig2IzckNyNJImFHRig3I0kiYkdGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GOjYjL0kkJWlkR0YoRjE=

Campo Vetorial

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJGR0YoLUknUlRBQkxFR0YoNiUiKlc4KCoqKiktSSdNQVRSSVhHRig2JTckNyMqJkkieEdGKCIiIkkieUdGKEY5NyMsJkY4RjlGOiEiIjckUSJ4RihRInlGKFEmZmllbGRGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GQjYjL0kkJWlkR0YoRjE=

Tabela 1 Os quatro tipos de vetores no pacote VectorCalculus

As estruturas de dados fornecidos nos pacotes VectorCalculus s\303\243o mais ricas e mais complexas do que as estruturas nos pacotes LinearAlgebra. A luz fundamental iluminando os pacotes VectorCalculus \303\251 a identifica\303\247\303\243o do ponto Cartesiano LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJiRidGNEY3Rj5GPkY+ com o vetor 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. Esta identifica\303\247\303\243o \303\251 \303\263bvia e inofensiva no plano Cartesiano, mas n\303\243o \303\251 poss\303\255vel em coordenadas n\303\243o Cartesianas. Qualquer confus\303\243o que os usu\303\241rios podem ter com os pacotes VectorCalculus no Maple geralmente decorre da falha de ver que essa identifica\303\247\303\243o do ponto e vetor \303\251 v\303\241lido somente em coordenadas Cartesianas.

Antes de esclarecer as diferen\303\247as entre estas quatro estruturas de dados, n\303\263s fazemos as seguintes observa\303\247\303\265es.

Cada uma das quatro estruturas de dados carrega, como um atributo, um sistema de coordenadas e onde possa ser aplic\303\241vel, os nomes das vari\303\241veis de coordenadas.

O sistema padr\303\243o \303\251 Cartesiano, mas os nomes para as vari\303\241veis de coordenadas n\303\243o s\303\243o definidas por padr\303\243o.

O comando SetCoordinates define um sistema de coordenadas ambiente (ou background).

O comando BasisFormat pode ser usado para suprimir a exibi\303\247\303\243o expl\303\255cita de vetores de base.

O comando About fornece informa\303\247\303\265es inerentes a uma dessas estruturas de dados.

O comando MapToBasis altera coordenadas nestas estruturas de dados.

<Text-field style="Heading 3" layout="Heading 3">Vetor Livre</Text-field>

O sistema de coordenadas padr\303\243o \303\251 Cartesiano, mas os nomes das vari\303\241veis de coordenadas n\303\243o s\303\243o definidas por padr\303\243o. Assim, para o vetor livre

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiVkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvJStleGVjdXRhYmxlR0Y0L0Y2USdub3JtYWxGJw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqQyVwKioqKS1JJ01BVFJJWEdGKDYkNyQ3I0kieEdGKDcjSSJ5R0YoNyRRInhGKFEieUYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY7NiMvSSQlaWRHRihGLw==

temos

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

Vector[column](2, {1 = x, 2 = y}, datatype = anything, storage = rectangular, order = Fortran_order, attributes = [coords = cartesian], shape = [])

ou melhor ainda,

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqa0UoKioqKS1JJ01BVFJJWEdGKDYjNyU3JEknVHlwZTp+R0YoSSxGcmVlflZlY3RvckdGKDckSS1Db21wb25lbnRzOn5HRig3JEkieEdGKEkieUdGKDckSS5Db29yZGluYXRlczp+R0YoSSpjYXJ0ZXNpYW5HRihJJ01hdHJpeEdGJTcjLUY/NiMvSSQlaWRHRihGLw==

O vetor livre V representa o ponto Cartesiano LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3Rj5GPkY+ e \303\251 identificado com a seta a partir da origem do plano Cartesiano ao ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3Rj5GPkY+. Esta identifica\303\247\303\243o do ponto e seta \303\251 tanto comum e inofensiva no plano Cartesiano.

Os vetores de base LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRInhGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRInlGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPQ== s\303\243o essencialmente os familiares LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiaUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiakYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjdGL0Y1Rjg=. Estes vetores de base podem ser suprimidos atrav\303\251s de

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEsQmFzaXNGb3JtYXRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiw2JVEmZmFsc2VGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRjsvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLyUrZXhlY3V0YWJsZUdGOkY7

nesse caso em o vetor livre \303\251 apresentado como um vetor coluna:

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqQyVwKioqKS1JJ01BVFJJWEdGKDYjNyQ3I0kieEdGKDcjSSJ5R0YoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY4NiMvSSQlaWRHRihGLw==

O vetor livre pode ser construido como um vetor linha com a sintaxe

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJXR0YoLUknUlRBQkxFR0YoNiUiKmtLKCoqKiktSSdWRUNUT1JHRig2IzckSSJ1R0YoSSJ2R0YoJkknVmVjdG9yR0YlNiNJJHJvd0dGKDcjLUY4NiMvSSQlaWRHRihGMQ==

Sua natureza como um vetor linha pode ser verificada com

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

Vector[row](2, {1 = u, 2 = v}, datatype = anything, storage = rectangular, order = Fortran_order, attributes = [coords = cartesian], shape = [])

Nos pacotes VectorCalculus, o ponto \303\251 estritamente o operador produto interno (ou escalar). N\303\243o h\303\241 reconhecimento de um produto externo nesses pacotes, como verificamos com os c\303\241lculos equivalentes

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYnUSJXRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPC1JI21vR0YkNi1RKSZtaWRkb3Q7RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHRjkvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGVS1GLDYnUSJWRidGNEY3RjpGPS8lK2V4ZWN1dGFibGVHRjlGQ0YrRmVuRkM= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYnUSJWRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPC1JI21vR0YkNi1RKSZtaWRkb3Q7RicvRjtRJ25vcm1hbEYnLyUmZmVuY2VHRjkvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGVS1GLDYnUSJXRidGNEY3RjpGPS8lK2V4ZWN1dGFibGVHRjlGQ0YrRmVuRkM=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqV2IoKioqKS1JJ01BVFJJWEdGKDYjNyQ3JComSSJ4R0YoIiIiSSJ1R0YoRjcqJkY2RjdJInZHRihGNzckKiZJInlHRihGN0Y4RjcqJkY9RjdGOkY3SSdNYXRyaXhHRiU3Iy1GPzYjL0kkJWlkR0YoRi8=

Os pacotes VectorCalculus n\303\243o tem um operador de transposi\303\247\303\243o. Se o comando Transpose do pacote LinearAlgebra \303\251 aplicado a V, obtemos o vetor linha

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJVR0YoLUknUlRBQkxFR0YoNiUiKmtvKCoqKiktSSdWRUNUT1JHRig2IzckSSJ4R0YoSSJ5R0YoJkknVmVjdG9yR0YlNiNJJHJvd0dGKDcjLUY4NiMvSSQlaWRHRihGMQ==

mas U agora \303\251 um vetor "LinearAlgebra" e perdeu o atributo que cont\303\251m as informa\303\247\303\265es de coordenadas, como vemos com

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

Vector[row](2, {1 = x, 2 = y}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

O comando MapToBasis \303\251 usado para modificar as coordenadas. Quando aplicado a um vetor livre, ele apenas muda as coordenadas de um ponto, e n\303\243o para um vetor. Assim, a lei contravariante para alterar as coordenadas em um vetor n\303\243o \303\251 aplicada ao vetor livre.

Para ilustrar, altere o vetor livre V para coordenadas polares, obtendo

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWcEdGKC1JJ1JUQUJMRUdGKDYlIipDJXkqKiopLUknTUFUUklYR0YoNiM3JDcjKiQpLCYqJClJInhHRigiIiMiIiJGPiokKUkieUdGKEY9Rj5GPiNGPkY9Rj43Iy1JJ2FyY3RhbkdGJTYkRkFGPCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GRzYjL0kkJWlkR0YoRjE=

O ponto Cartesiano LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3Rj5GPkY+ tornou-se o ponto polar 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 Nenhuma altera\303\247\303\243o de vetores de base ocorreu.

Em termos de "vetores de base" expl\303\255cito, ter\303\255amos

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYnUSNWcEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjxGNC8lK2V4ZWN1dGFibGVHRjlGOkY9RitGPy9GO1Enbm9ybWFsRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqQyV5KioqKS1JJ01BVFJJWEdGKDYkNyQ3IyokKSwmKiQpSSJ4R0YoIiIjIiIiRjwqJClJInlHRihGO0Y8RjwjRjxGO0Y8NyMtSSdhcmN0YW5HRiU2JEY/Rjo3JFEickYoUSZ0aGV0YUYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZINiMvSSQlaWRHRihGLw==

Os s\303\255mbolos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRInJGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRJyYjOTUyO0YnL0YzUSZmYWxzZUYnL0Y2USdub3JtYWxGJ0Y/LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGPw== n\303\243o s\303\243o transformados covariantemente como vetores de base. Eles apenas indicam o sistema de coordenadas em que interpretam o que s\303\243o essencialmente coordenadas de um ponto. A identifica\303\247\303\243o do ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3Rj5GPkY+ com o vetor 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 mant\303\251m apenas no plano cartesiano. Ele n\303\243o se estende a coordenadas n\303\243o Cartesianas.

Pode-se pensar em uma estrutura retangular na qual os eixos das coordenadas representam LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= (horizontalmente) e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy (verticalmente). Quando a transforma\303\247\303\243o de Cartesianas para coordenadas polares \303\251 interpretada como um mapeamento, o ponto Cartesiano LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3Rj5GPkY+ \303\251 fisicamente mapeado para o ponto polar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUScmIzk1MjtGJy9GNUZCRj5GPkY+Rj4= que reside no LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUScmIzk1MjtGJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRidGOg==-plano retangular. Quando a transforma\303\247\303\243o de Cartesiana para coordenadas polares \303\251 interpretada como uma mudan\303\247a de coordenadas, o ponto Cartesiano LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJ5RidGNEY3Rj5GPkY+ permanece fixo, mas seu endere\303\247o \303\251 alterado conforme as coordenadas impostas pelos c\303\255rculos conc\303\252ntricos e linhas radiais puxadas de volta para o plano Cartesiano do plano "polar".

A figura 1 ilustra um experimento simples, em que MapToBasis \303\251 aplicado ao vetor livre Cartesiano 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. Ap\303\263s a convers\303\243o para coordenadas polares, o "vetor" mant\303\251m a sua correspond\303\252ncia com o ponto em que ele \303\251 desenhado. O "vetor" transformado, representado graficamente atrav\303\251s do comando PlotVector, parece inalterado.

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

Figura 1 MapToBasis aplicado ao vetor livre 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

<Text-field style="Heading 3" layout="Heading 3">PositionVector</Text-field>

Curvas e superf\303\255cies incorporados em um espa\303\247o Cartesiano s\303\243o freq\303\274entemente descritos com a nota\303\247\303\243o de vetor posi\303\247\303\243o

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUC1GLDYlUSJ4RicvRjNGMS9GNlEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJ1RidGVkZXLUY7Ni1RIixGJ0Y+RkAvRkNGMUZERkZGSEZKRkwvRk9RJjAuMGVtRicvRlJRLDAuMzMzMzMzM2VtRictRiw2JVEidkYnRlZGV0Y+Rj4tRjs2LVEifkYnRj5GQEZCRkRGRkZIRkpGTEZfby9GUkZgby1GLDYnUSJpRidGL0YyRjVGOC1GOzYtUSIrRidGPkZARkJGREZGRkhGSkZML0ZPUSwwLjIyMjIyMjJlbUYnL0ZSRmFwLUYsNiVRInlGJ0ZWRldGWUZmby1GLDYnUSJqRidGL0YyRjVGOEZdcC1GLDYlUSJ6RidGVkZXRllGZm8tRiw2J1Eia0YnRi9GMkY1RjhGPg==

Consequentemente, os pacotes VectorCalculus fornecem o comando PositionVector. Por exemplo, a par\303\241bola dada parametricamente por 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 \303\251 capturada com

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLUknUlRBQkxFR0YoNiUiKmtHKSoqKiktSSdNQVRSSVhHRig2IzckNyNJInRHRig3IyokKUY3IiIjIiIiJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY9NiMvSSQlaWRHRihGMQ==

O VetorPosi\303\247\303\243o sempre ecoa como um vetor coluna, e sempre representa um vetor em coordenadas Cartesianas. Por meio do comando PlotPositionVector, a Figura 2 apresenta um gr\303\241fico da curva resultante.

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

-%%PLOTG6%-%'CURVESG6%7dw7$$!#5!""$"#5!""7$$!0\(\**y%[*)*!#:$"0)*=a\,3z*!#:7$$!0[&4>cN.)*!#:$"04X%R"y0h*!#:7$$!0_/4)HY+(*!#:$"0"**Q/#)*)4%*!#:7$$!0f<NI))of*!#:$"0F>5^E+@*!#:7$$!0Y#\)*e!Q\*!#:$"0.DQ/NK,*!#:7$$!0%yc8`B)R*!#:$"0O>4q#oK))!#:7$$!0rU&3vF*H*!#:$"0%))3=ilZ')!#:7$$!08D]?Np>*!#:$"00Vlrh$e%)!#:7$$!0'Gd96#\4*!#:$"0LI!3!f<F)!#:7$$!04<M3()**)*)!#:$"/1+wn)>3)!#97$$!0He;8hv*))!#:$"0kf"4%fm"z!#:7$$!0.05S6Nz)!#:$"0agfF%eKx!#:7$$!/3;KW.*o)!#9$"/wKO>$*\v!#97$$!0%yc8:N)e)!#:$"/.1s"yfP(!#97$$!0X*)yx@p\)!#:$"/s&*pzw>s!#97$$!0Z%*)yH?)Q)!#:$"0T8:#\>Oq!#:7$$!0Rxa*Q5'H)!#:$"0^bW)R`#)o!#:7$$!0<Mowq*)=)!#:$"0Y1?ACfq'!#:7$$!0)[(\zRT4)!#:$"0ff?!*4:b'!#:7$$!0sW*)=&4!*z!#:$"0wRG6iTQ'!#:7$$!0*zf>,-"*y!#:$"0.!z_)>oA'!#:7$$!0'>Ryck(y(!#:$"/x@@Dukg!#97$$!0yc8n:Fp(!#:$"0#Q.Suy<f!#:7$$!0&3<M3K!f(!#:$"0"[cOqHhd!#:7$$!/%zePhR[(!#9$"0Zlvyn4g&!#:7$$!0(Qxa^P"R(!#:$"0%3'ymUKY&!#:7$$!0\(\*\z8H(!#:$"0Ap0]@kJ&!#:7$$!03:I?u!)=(!#:$"030[2To;&!#:7$$!07BY75q3(!#:$"00^1DrD-&!#:7$$!/3;KaA*)p!#9$"0McT@F\)[!#:7$$!03:I?_1)o!#:$"0i&)QZPVt%!#:7$$!0>QwK%4$y'!#:$"0ujd'o.,Y!#:7$$!0"=Os/$*ym!#:$"0JkaA63Y%!#:7$$!0W)oPDa%e'!#:$"0'G1V+iNV!#:7$$!0&)pRf^8['!#:$"0bl%[=z+U!#:7$$!0&*)ydpD%Q'!#:$"0m2.pte2%!#:7$$!0;Kk3lFG'!#:$"04HJr8t%R!#:7$$!0yb6BQN='!#:$"0^;c]9O#Q!#:7$$!0uZ&4plzg!#:$"0;"y8GA'p$!#:7$$!0E^-&ogzf!#:$"0<d$3)pbd$!#:7$$!0NqS@"Hxe!#:$"0&))\,_DaM!#:7$$!02:I!G#ex&!#:$"0*G=0H,OL!#:7$$!0yc8(Qe#o&!#:$"0U+b%f<HK!#:7$$!0MoO`@dd&!#:$"0G,@1n)3J!#:7$$!0iC\eU,[&!#:$"0V5^F'>.I!#:7$$!0E_/\N#y`!#:$"0.w!*pTD*G!#:7$$!0&**)zR(p!G&!#:$"0y84]w&)y#!#:7$$!0.29)QRs^!#:$"0pTk%eOvE!#:7$$!0&)pR*4hy]!#:$"092G'*G#zD!#:7$$!0X*)ydm@(\!#:$"04Gy/WAZ#!#:7$$!0@T#[S:v[!#:$"0E3%*p7nP#!#:7$$!0nMpeP!pZ!#:$"0df0&>PuA!#:7$$!0oNr-xun%!#:$"/#QR8zy=#!#97$$!0$f=P-?tX!#:$"0uR4/;94#!#:7$$!0:Ig+uCZ%!#:$"0ahMP-.+#!#:7$$!0U%)od8=P%!#:$"/J5&Rv7">!#97$$!0['HfM_rU!#:$"0-KjE"fC=!#:7$$!0LmK0w^<%!#:$"0'od2&4Ku"!#:7$$!0*)yd&>-rS!#:$"0QVk(>Kd;!#:7$$!0sV([bvrR!#:$"0l(*Q@%[x:!#:7$$!0C['HBGnQ!#:$"0&4shse&\"!#:7$$!0rU&3*3Fx$!#:$"0wf3DLLU"!#:7$$!0NpQd(=oO!#:$"0&*3x+gbM"!#:7$$!0sV([V2oN!#:$"0H;eX:JF"!#:7$$!005?![?oM!#:$"0co[XWG?"!#:7$$!0$oOt1*QO$!#:$"0WOi/w:8"!#:7$$!0#Qw_N"yE$!#:$"0pi:agy1"!#:7$$!0)f>RuTpJ!#:$"0'zQ!p?X+"!#:7$$!0&4>QkxgI!#:$"/\e/CNo$*!#:7$$!0w_0"4TiH!#:$"01iHSyex)!#;7$$!0MoOt8='G!#:$"0t7i%y(**=)!#;7$$!/*zf**3&fF!#9$"0*R*))*)*)[h(!#;7$$!0&3<M5ZlE!#:$"0%Q+Met/r!#;7$$!/.17'H_c#!#9$"0/"fiHS!e'!#;7$$!0&3<M7vlC!#:$"04:)["H*zg!#;7$$!0Hd9HS$fB!#:$"0v$*3h'[mb!#;7$$!06@UCPaE#!#:$"07/v!f?K^!#;7$$!0`06i#4d@!#:$"0"z-w&[Il%!#;7$$!0ze<&*>$f?!#:$"0%=rj')zSU!#;7$$!0:Ig+zD'>!#:$"0H5\N;<&Q!#;7$$!0Gb5T^&e=!#:$"0cNvM8UX$!#;7$$!03:I+.Tv"!#:$"/l=Xt(o2$!#:7$$!0V&3</2f;!#:$"0,[)[Y^_F!#;7$$!/3;K+:e:!#9$"0rAF_JyU#!#;7$$!);mf9!")$"0c9l)>hI@!#;7$$!0^-05**GN"!#:$"0^Sh(fLI=!#;7$$!0Qw_&)>0E"!#:$"0*fa0."*)e"!#;7$$!0MoO$*=W:"!#:$"0&>TuIoK8!#;7$$!0CZ%*[yY0"!#:$"/F5;nM76!#:7$$!0Hd9H9!f&*!#;$"0ZGCUvu8*!#<7$$!0uZ&4zXq&)!#;$"0$H$z([FXt!#<7$$!0Pu[(H>iv!#;$"0$R#*ein=d!#<7$$!0)e<N!\M\'!#;$"0mUs.)[;U!#<7$$!0W([(\:N^&!#;$"0U.TJ&))RI!#<7$$!0nJjE&>YX!#;$"0kh*R"*ym?!#<7$$!0\'Hfe97N!#;$"0N(p`o^L7!#<7$$!0=Pu[Z.[#!#;$"0&fVeO7_h!#=7$$!0Rze<ZUb"!#;$"00HPG%o:C!#=7$$!0<V'Gd9sX!#<$".&Rc;X!4#!#<7$$"0Cf=P9tg%!#<$"029@dMF7#!#>7$$"0/5?SsV`"!#;$"02]!o')HaB!#=7$$"0LnMpe!fD!#;$"0s5mR"y[l!#=7$$"0V([(\")RZ$!#;$"/&)[WZ&o?"!#;7$$".(Rzy!H]%!#9$"0cLq$zhF?!#<7$$"0LmKla'Qb!#;$"0(["o`pw1$!#<7$$"0e<Nqy%pl!#;$"06(fV]!eJ%!#<7$$"0"Qw_X=Dv!#;$"/bJb-%Gm&!#;7$$"04:IgiZ^)!#;$"0Vq&=#=,D(!#<7$$"0&4>Qc=Q&*!#;$"0Afo_)p(4*!#<7$$"0OrUlKe0"!#:$"/d#Qf#y96!#:7$$"08Faom2;"!#:$"/v*zHztM"!#:7$$"0$f=PE>`7!#:$"0-(*ey"\q:!#;7$$"/#RyOUsN"!#9$"0vd]%o5U=!#;7$$"0U$oO$><Y"!#:$"0@M#>MiO@!#;7$$"0Qw_D-Cc"!#:$"0t#H235TC!#;7$$"0xa4*>$Ql"!#:$"0V0VDg^t#!#;7$$"0v\**y]Dw"!#:$"0[_rG&e1J!#;7$$"0$oOt)\Y&=!#:$"0hzF:E(RM!#;7$$"005?+$yh>!#:$"0dvpa#f[Q!#;7$$"0NpQ(Rhc?!#:$"0n9v.h'HU!#;7$$"/&**)z&e1;#!#9$"0J$*))\X%oY!#;7$$"0BY#\OtfA!#:$"0pNb;'R1^!#;7$$"0E_/43JO#!#:$"0$4;Z)zUe&!#;7$$"0W([(4Q!eC!#:$"0n*p)G^>/'!#;7$$"0PtY$HVgD!#:$"02gH"o"eb'!#;7$$"0$['HR#zmE!#:$"01vrm"y6r!#;7$$"0NqShy$fF!#:$"0$))yN.<9w!#;7$$"0tY$pUPfG!#:$"0;-A@@g<)!#;7$$"09HeczE'H!#:$"0d"y4-Zx()!#;7$$"06@UkVP1$!#:$"0A0v6DlQ*!#;7$$"0U$oO$G:;$!#:$"0@_OUh_***!#;7$$"0:Hec,,F$!#:$"0#Q3DkNp5!#:7$$"0.17WfwO$!#:$"0T%>6I6M6!#:7$$"0T#['HB=Z$!#:$"/)*>+dN07!#97$$"0yb6B6ic$!#:$"0;AXD'yr7!#:7$$"0Pu[<-%pO!#:$"0G(4K7XY8!#:7$$"0Gb5"o\mP!#:$"0'*oF#)\'=9!#:7$$"017Co))z'Q!#:$"0yEZkLh\"!#:7$$"0W)oPb@nR!#:$"0mZA"*zQd"!#:7$$"0['Hfo4rS!#:$"0PxP'HQd;!#:7$$"0(Hf=p9rT!#:$"0w[;mY)R<!#:7$$"0(QxaDYtU!#:$"0W02A[i#=!#:7$$"0:He'4$\P%!#:$"03xb4-S">!#:7$$"0W([(*)p"oW!#:$"0H"GBUX'*>!#:7$$"0)e<NA.vX!#:$"0%)*G&*>4$4#!#:7$$"/'>R=61n%!#9$"0[NJ)3Y"=#!#:7$$"0'>Ry#=Dx%!#:$"0ae<2$pxA!#:7$$"0Fa3Pc+([!#:$"0$)Hb!\urB!#:7$$"0=Pu))f$y\!#:$"0O%)or1%yC!#:7$$"0Pu[xU@2&!#:$"0.rGBjEd#!#:7$$"0xa4>(ey^!#:$"03K%Hlx"o#!#:7$$"0,.1s*fv_!#:$"0m-7C&>$y#!#:7$$"0b4>=;<Q&!#:$"0rii!pG'*G!#:7$$"0a3<uwKZ&!#:$"0xK"Hen&*H!#:7$$"0He;``vd&!#:$"0R^)R."46$!#:7$$"029Gwz#yc!#:$"0Qyk5'GCK!#:7$$"/)f>>S*yd!#9$"0%[Au\hRL!#:7$$"0uZ&4.Bze!#:$"0[qK!\`cM!#:7$$"0*yd:xdvf!#:$"06"\.HvqN!#:7$$"0LlI"=tzg!#:$"0')z=*QJ'p$!#:7$$"/05?#)**yh!#9$"0_+/!>+=Q!#:7$$"0)f>R9Z$G'!#:$"0;>FL,#[R!#:7$$"0^,.'[/yj!#:$"0&=+Cc%z1%!#:7$$"0([(\>mD['!#:$"/JAZkO-U!#97$$"/05?%zEe'!#9$"0Z"yMo;LV!#:7$$"0<Mo'*[Do'!#:$"0l8%pgklW!#:7$$"0Rxa4joy'!#:$"0Hvw1^hg%!#:7$$"//3;-%H)o!#9$"0p8=g'[PZ!#:7$$"0C['HjL")p!#:$"0kmZp0R([!#:7$$"0F`1Lx**3(!#:$"0s<\&yxE]!#:7$$"0Y"HeGM)=(!#:$"0)\$[IFs;&!#:7$$"0)e<N+%*)G(!#:$"0(*QOokGJ&!#:7$$"0KkGxW7R(!#:$"0UR#H*\IY&!#:7$$"0PtYt#G&[(!#:$"0#**zhd%Hg&!#:7$$"0#RycT_&e(!#:$"0C:Ln<Sv&!#:7$$"0PtY`-]o(!#:$"0h$z&REf!f!#:7$$"0$pQxMT"z(!#:$"0ogvR712'!#:7$$"07BY_;`)y!#:$"0W\$p;#y@'!#:7$$"/(Qx9hO*z!#9$"0r'[a=')*Q'!#:7$$"0V&3<QV"4)!#:$"0OF;7Ira'!#:7$$"029Gwu")=)!#:$"0`QYf?Yq'!#:7$$"0&*)ydB?#H)!#:$"01_U*>1wo!#:7$$"0:Hew]mR)!#:$"0#*H$3WP]q!#:7$$"0ze<N$o"\)!#:$"0v`Yho3@(!#:7$$"0U$oOPg#f)!#:$"0emv*QG$Q(!#:7$$"0AW)o@4"p)!#:$"0`M(3$3Nb(!#:7$$"0rT$oY&yz)!#:$"/i_wYASx!#97$$"0%yc8RB!*))!#:$"0<&z.fi.z!#:7$$"0)e<N[L'**)!#:$"/*fm//M4)!#97$$"0*pRz_2'4*!#:$"/d%)[&eQF)!#97$$"0\)pRB&[>*!#:$"0*e)[&4`a%)!#:7$$"0X*)y(zq$H*!#:$"/'Gyz+tj)!#97$$"0yc8ZMXR*!#:$"04^LzFd#))!#:7$$"0jE`')39]*!#:$"0v5E/xw-*!#:7$$"0[&4>AS*f*!#:$"0_(R'H_[@*!#:7$$"016ACMhp*!#:$"0y(HC>],%*!#:7$$"0d9H=R&*z*!#:$"/yu>o4.'*!#97$$"/05?!>F!**!#9$"0-1"*R%Q1)*!#:7$$"#5!""$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"$?"!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%]M!""-%)CHILDRENG6"

Figura 2 Gr\303\241fico de uma curva descrita em nota\303\247\303\243o de vetor posi\303\247\303\243o

O comando PlotPositionVector tamb\303\251m ir\303\241 representar graficamente v\303\241rios campos vetoriais ao longo da curva. No gr\303\241fico na Figura 2, Figura 3 mostra os vetores normais principais (em verde).

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

-%%PLOTG6/-%'CURVESG6%7dw7$$!#5!""$"#5!""7$$!0\(\**y%[*)*!#:$"0)*=a\,3z*!#:7$$!0[&4>cN.)*!#:$"04X%R"y0h*!#:7$$!0_/4)HY+(*!#:$"0"**Q/#)*)4%*!#:7$$!0f<NI))of*!#:$"0F>5^E+@*!#:7$$!0Y#\)*e!Q\*!#:$"0.DQ/NK,*!#:7$$!0%yc8`B)R*!#:$"0O>4q#oK))!#:7$$!0rU&3vF*H*!#:$"0%))3=ilZ')!#:7$$!08D]?Np>*!#:$"00Vlrh$e%)!#:7$$!0'Gd96#\4*!#:$"0LI!3!f<F)!#:7$$!04<M3()**)*)!#:$"/1+wn)>3)!#97$$!0He;8hv*))!#:$"0kf"4%fm"z!#:7$$!0.05S6Nz)!#:$"0agfF%eKx!#:7$$!/3;KW.*o)!#9$"/wKO>$*\v!#97$$!0%yc8:N)e)!#:$"/.1s"yfP(!#97$$!0X*)yx@p\)!#:$"/s&*pzw>s!#97$$!0Z%*)yH?)Q)!#:$"0T8:#\>Oq!#:7$$!0Rxa*Q5'H)!#:$"0^bW)R`#)o!#:7$$!0<Mowq*)=)!#:$"0Y1?ACfq'!#:7$$!0)[(\zRT4)!#:$"0ff?!*4:b'!#:7$$!0sW*)=&4!*z!#:$"0wRG6iTQ'!#:7$$!0*zf>,-"*y!#:$"0.!z_)>oA'!#:7$$!0'>Ryck(y(!#:$"/x@@Dukg!#97$$!0yc8n:Fp(!#:$"0#Q.Suy<f!#:7$$!0&3<M3K!f(!#:$"0"[cOqHhd!#:7$$!/%zePhR[(!#9$"0Zlvyn4g&!#:7$$!0(Qxa^P"R(!#:$"0%3'ymUKY&!#:7$$!0\(\*\z8H(!#:$"0Ap0]@kJ&!#:7$$!03:I?u!)=(!#:$"030[2To;&!#:7$$!07BY75q3(!#:$"00^1DrD-&!#:7$$!/3;KaA*)p!#9$"0McT@F\)[!#:7$$!03:I?_1)o!#:$"0i&)QZPVt%!#:7$$!0>QwK%4$y'!#:$"0ujd'o.,Y!#:7$$!0"=Os/$*ym!#:$"0JkaA63Y%!#:7$$!0W)oPDa%e'!#:$"0'G1V+iNV!#:7$$!0&)pRf^8['!#:$"0bl%[=z+U!#:7$$!0&*)ydpD%Q'!#:$"0m2.pte2%!#:7$$!0;Kk3lFG'!#:$"04HJr8t%R!#:7$$!0yb6BQN='!#:$"0^;c]9O#Q!#:7$$!0uZ&4plzg!#:$"0;"y8GA'p$!#:7$$!0E^-&ogzf!#:$"0<d$3)pbd$!#:7$$!0NqS@"Hxe!#:$"0&))\,_DaM!#:7$$!02:I!G#ex&!#:$"0*G=0H,OL!#:7$$!0yc8(Qe#o&!#:$"0U+b%f<HK!#:7$$!0MoO`@dd&!#:$"0G,@1n)3J!#:7$$!0iC\eU,[&!#:$"0V5^F'>.I!#:7$$!0E_/\N#y`!#:$"0.w!*pTD*G!#:7$$!0&**)zR(p!G&!#:$"0y84]w&)y#!#:7$$!0.29)QRs^!#:$"0pTk%eOvE!#:7$$!0&)pR*4hy]!#:$"092G'*G#zD!#:7$$!0X*)ydm@(\!#:$"04Gy/WAZ#!#:7$$!0@T#[S:v[!#:$"0E3%*p7nP#!#:7$$!0nMpeP!pZ!#:$"0df0&>PuA!#:7$$!0oNr-xun%!#:$"/#QR8zy=#!#97$$!0$f=P-?tX!#:$"0uR4/;94#!#:7$$!0:Ig+uCZ%!#:$"0ahMP-.+#!#:7$$!0U%)od8=P%!#:$"/J5&Rv7">!#97$$!0['HfM_rU!#:$"0-KjE"fC=!#:7$$!0LmK0w^<%!#:$"0'od2&4Ku"!#:7$$!0*)yd&>-rS!#:$"0QVk(>Kd;!#:7$$!0sV([bvrR!#:$"0l(*Q@%[x:!#:7$$!0C['HBGnQ!#:$"0&4shse&\"!#:7$$!0rU&3*3Fx$!#:$"0wf3DLLU"!#:7$$!0NpQd(=oO!#:$"0&*3x+gbM"!#:7$$!0sV([V2oN!#:$"0H;eX:JF"!#:7$$!005?![?oM!#:$"0co[XWG?"!#:7$$!0$oOt1*QO$!#:$"0WOi/w:8"!#:7$$!0#Qw_N"yE$!#:$"0pi:agy1"!#:7$$!0)f>RuTpJ!#:$"0'zQ!p?X+"!#:7$$!0&4>QkxgI!#:$"/\e/CNo$*!#:7$$!0w_0"4TiH!#:$"01iHSyex)!#;7$$!0MoOt8='G!#:$"0t7i%y(**=)!#;7$$!/*zf**3&fF!#9$"0*R*))*)*)[h(!#;7$$!0&3<M5ZlE!#:$"0%Q+Met/r!#;7$$!/.17'H_c#!#9$"0/"fiHS!e'!#;7$$!0&3<M7vlC!#:$"04:)["H*zg!#;7$$!0Hd9HS$fB!#:$"0v$*3h'[mb!#;7$$!06@UCPaE#!#:$"07/v!f?K^!#;7$$!0`06i#4d@!#:$"0"z-w&[Il%!#;7$$!0ze<&*>$f?!#:$"0%=rj')zSU!#;7$$!0:Ig+zD'>!#:$"0H5\N;<&Q!#;7$$!0Gb5T^&e=!#:$"0cNvM8UX$!#;7$$!03:I+.Tv"!#:$"/l=Xt(o2$!#:7$$!0V&3</2f;!#:$"0,[)[Y^_F!#;7$$!/3;K+:e:!#9$"0rAF_JyU#!#;7$$!);mf9!")$"0c9l)>hI@!#;7$$!0^-05**GN"!#:$"0^Sh(fLI=!#;7$$!0Qw_&)>0E"!#:$"0*fa0."*)e"!#;7$$!0MoO$*=W:"!#:$"0&>TuIoK8!#;7$$!0CZ%*[yY0"!#:$"/F5;nM76!#:7$$!0Hd9H9!f&*!#;$"0ZGCUvu8*!#<7$$!0uZ&4zXq&)!#;$"0$H$z([FXt!#<7$$!0Pu[(H>iv!#;$"0$R#*ein=d!#<7$$!0)e<N!\M\'!#;$"0mUs.)[;U!#<7$$!0W([(\:N^&!#;$"0U.TJ&))RI!#<7$$!0nJjE&>YX!#;$"0kh*R"*ym?!#<7$$!0\'Hfe97N!#;$"0N(p`o^L7!#<7$$!0=Pu[Z.[#!#;$"0&fVeO7_h!#=7$$!0Rze<ZUb"!#;$"00HPG%o:C!#=7$$!0<V'Gd9sX!#<$".&Rc;X!4#!#<7$$"0Cf=P9tg%!#<$"029@dMF7#!#>7$$"0/5?SsV`"!#;$"02]!o')HaB!#=7$$"0LnMpe!fD!#;$"0s5mR"y[l!#=7$$"0V([(\")RZ$!#;$"/&)[WZ&o?"!#;7$$".(Rzy!H]%!#9$"0cLq$zhF?!#<7$$"0LmKla'Qb!#;$"0(["o`pw1$!#<7$$"0e<Nqy%pl!#;$"06(fV]!eJ%!#<7$$"0"Qw_X=Dv!#;$"/bJb-%Gm&!#;7$$"04:IgiZ^)!#;$"0Vq&=#=,D(!#<7$$"0&4>Qc=Q&*!#;$"0Afo_)p(4*!#<7$$"0OrUlKe0"!#:$"/d#Qf#y96!#:7$$"08Faom2;"!#:$"/v*zHztM"!#:7$$"0$f=PE>`7!#:$"0-(*ey"\q:!#;7$$"/#RyOUsN"!#9$"0vd]%o5U=!#;7$$"0U$oO$><Y"!#:$"0@M#>MiO@!#;7$$"0Qw_D-Cc"!#:$"0t#H235TC!#;7$$"0xa4*>$Ql"!#:$"0V0VDg^t#!#;7$$"0v\**y]Dw"!#:$"0[_rG&e1J!#;7$$"0$oOt)\Y&=!#:$"0hzF:E(RM!#;7$$"005?+$yh>!#:$"0dvpa#f[Q!#;7$$"0NpQ(Rhc?!#:$"0n9v.h'HU!#;7$$"/&**)z&e1;#!#9$"0J$*))\X%oY!#;7$$"0BY#\OtfA!#:$"0pNb;'R1^!#;7$$"0E_/43JO#!#:$"0$4;Z)zUe&!#;7$$"0W([(4Q!eC!#:$"0n*p)G^>/'!#;7$$"0PtY$HVgD!#:$"02gH"o"eb'!#;7$$"0$['HR#zmE!#:$"01vrm"y6r!#;7$$"0NqShy$fF!#:$"0$))yN.<9w!#;7$$"0tY$pUPfG!#:$"0;-A@@g<)!#;7$$"09HeczE'H!#:$"0d"y4-Zx()!#;7$$"06@UkVP1$!#:$"0A0v6DlQ*!#;7$$"0U$oO$G:;$!#:$"0@_OUh_***!#;7$$"0:Hec,,F$!#:$"0#Q3DkNp5!#:7$$"0.17WfwO$!#:$"0T%>6I6M6!#:7$$"0T#['HB=Z$!#:$"/)*>+dN07!#97$$"0yb6B6ic$!#:$"0;AXD'yr7!#:7$$"0Pu[<-%pO!#:$"0G(4K7XY8!#:7$$"0Gb5"o\mP!#:$"0'*oF#)\'=9!#:7$$"017Co))z'Q!#:$"0yEZkLh\"!#:7$$"0W)oPb@nR!#:$"0mZA"*zQd"!#:7$$"0['Hfo4rS!#:$"0PxP'HQd;!#:7$$"0(Hf=p9rT!#:$"0w[;mY)R<!#:7$$"0(QxaDYtU!#:$"0W02A[i#=!#:7$$"0:He'4$\P%!#:$"03xb4-S">!#:7$$"0W([(*)p"oW!#:$"0H"GBUX'*>!#:7$$"0)e<NA.vX!#:$"0%)*G&*>4$4#!#:7$$"/'>R=61n%!#9$"0[NJ)3Y"=#!#:7$$"0'>Ry#=Dx%!#:$"0ae<2$pxA!#:7$$"0Fa3Pc+([!#:$"0$)Hb!\urB!#:7$$"0=Pu))f$y\!#:$"0O%)or1%yC!#:7$$"0Pu[xU@2&!#:$"0.rGBjEd#!#:7$$"0xa4>(ey^!#:$"03K%Hlx"o#!#:7$$"0,.1s*fv_!#:$"0m-7C&>$y#!#:7$$"0b4>=;<Q&!#:$"0rii!pG'*G!#:7$$"0a3<uwKZ&!#:$"0xK"Hen&*H!#:7$$"0He;``vd&!#:$"0R^)R."46$!#:7$$"029Gwz#yc!#:$"0Qyk5'GCK!#:7$$"/)f>>S*yd!#9$"0%[Au\hRL!#:7$$"0uZ&4.Bze!#:$"0[qK!\`cM!#:7$$"0*yd:xdvf!#:$"06"\.HvqN!#:7$$"0LlI"=tzg!#:$"0')z=*QJ'p$!#:7$$"/05?#)**yh!#9$"0_+/!>+=Q!#:7$$"0)f>R9Z$G'!#:$"0;>FL,#[R!#:7$$"0^,.'[/yj!#:$"0&=+Cc%z1%!#:7$$"0([(\>mD['!#:$"/JAZkO-U!#97$$"/05?%zEe'!#9$"0Z"yMo;LV!#:7$$"0<Mo'*[Do'!#:$"0l8%pgklW!#:7$$"0Rxa4joy'!#:$"0Hvw1^hg%!#:7$$"//3;-%H)o!#9$"0p8=g'[PZ!#:7$$"0C['HjL")p!#:$"0kmZp0R([!#:7$$"0F`1Lx**3(!#:$"0s<\&yxE]!#:7$$"0Y"HeGM)=(!#:$"0)\$[IFs;&!#:7$$"0)e<N+%*)G(!#:$"0(*QOokGJ&!#:7$$"0KkGxW7R(!#:$"0UR#H*\IY&!#:7$$"0PtYt#G&[(!#:$"0#**zhd%Hg&!#:7$$"0#RycT_&e(!#:$"0C:Ln<Sv&!#:7$$"0PtY`-]o(!#:$"0h$z&REf!f!#:7$$"0$pQxMT"z(!#:$"0ogvR712'!#:7$$"07BY_;`)y!#:$"0W\$p;#y@'!#:7$$"/(Qx9hO*z!#9$"0r'[a=')*Q'!#:7$$"0V&3<QV"4)!#:$"0OF;7Ira'!#:7$$"029Gwu")=)!#:$"0`QYf?Yq'!#:7$$"0&*)ydB?#H)!#:$"01_U*>1wo!#:7$$"0:Hew]mR)!#:$"0#*H$3WP]q!#:7$$"0ze<N$o"\)!#:$"0v`Yho3@(!#:7$$"0U$oOPg#f)!#:$"0emv*QG$Q(!#:7$$"0AW)o@4"p)!#:$"0`M(3$3Nb(!#:7$$"0rT$oY&yz)!#:$"/i_wYASx!#97$$"0%yc8RB!*))!#:$"0<&z.fi.z!#:7$$"0)e<N[L'**)!#:$"/*fm//M4)!#97$$"0*pRz_2'4*!#:$"/d%)[&eQF)!#97$$"0\)pRB&[>*!#:$"0*e)[&4`a%)!#:7$$"0X*)y(zq$H*!#:$"/'Gyz+tj)!#97$$"0yc8ZMXR*!#:$"04^LzFd#))!#:7$$"0jE`')39]*!#:$"0v5E/xw-*!#:7$$"0[&4>AS*f*!#:$"0_(R'H_[@*!#:7$$"016ACMhp*!#:$"0y(HC>],%*!#:7$$"0d9H=R&*z*!#:$"/yu>o4.'*!#97$$"/05?!>F!**!#9$"0-1"*R%Q1)*!#:7$$"#5!""$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%)POLYGONSG6'7&7$$!+v,b7z!#5$"*G!3gi!"*7$$!+D)\u3)!#5$"*s>*Rl!"*7$$!*Oh5K#!"*$"+^7R95!"*7$$!*rhh9#!"*$"+tI2k)*!#57%7$$!*t!)ej#!"*$"*NiZ1"!")7$$")/$)*z%!"*$"*%*)**p6!")7$$!*MU8$=!"*$"+"3i.O*!#5-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$!+v,b7z!#5$"*G!3gi!"*7$$!+D)\u3)!#5$"*s>*Rl!"*7$$!*Oh5K#!"*$"+^7R95!"*7$$!*t!)ej#!"*$"*NiZ1"!")7$$")/$)*z%!"*$"*%*)**p6!")7$$!*MU8$=!"*$"+"3i.O*!#57$$!*rhh9#!"*$"+tI2k)*!#57$$!+v,b7z!#5$"*G!3gi!"*-%)POLYGONSG6'7&7$$!+Ym:rQ!#5$"+<`#p\"!#57$$!+aL%)GT!#5$"+$ouIq"!#57$$"*oH3>"!#5$"+'e#)H,(!#57$$"*w'pnP!#5$"*ALo!o!"*7%7$$!*/JvW$!#5$"+W90%Q(!#57$$"+u/&pC#!#5$"+#4)o3%*!#57$$"*[dgS)!#5$"+iVwNk!#5-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$!+Ym:rQ!#5$"+<`#p\"!#57$$!+aL%)GT!#5$"+$ouIq"!#57$$"*oH3>"!#5$"+'e#)H,(!#57$$!*/JvW$!#5$"+W90%Q(!#57$$"+u/&pC#!#5$"+#4)o3%*!#57$$"*[dgS)!#5$"+iVwNk!#57$$"*w'pnP!#5$"*ALo!o!"*7$$!+Ym:rQ!#5$"+<`#p\"!#5-%)POLYGONSG6'7&7$$"$l"!"%$""!!""7$$!$l"!"%$""!!""7$$!$l"!"%$"#o!"#7$$"$l"!"%$"#o!"#7%7$$!$f(!"%$"#o!"#7$$""!!""$"#5!""7$$"$f(!"%$"#o!"#-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"$l"!"%$""!!""7$$!$l"!"%$""!!""7$$!$l"!"%$"#o!"#7$$!$f(!"%$"#o!"#7$$""!!""$"#5!""7$$"$f(!"%$"#o!"#7$$"$l"!"%$"#o!"#7$$"$l"!"%$""!!""-%)POLYGONSG6'7&7$$"+aL%)GT!#5$"+$ouIq"!#57$$"+Ym:rQ!#5$"+<`#p\"!#57$$!*w'pnP!#5$"*ALo!o!"*7$$!*oH3>"!#5$"+'e#)H,(!#57%7$$!*[dgS)!#5$"+iVwNk!#57$$!+u/&pC#!#5$"+#4)o3%*!#57$$"*/JvW$!#5$"+W90%Q(!#5-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"+aL%)GT!#5$"+$ouIq"!#57$$"+Ym:rQ!#5$"+<`#p\"!#57$$!*w'pnP!#5$"*ALo!o!"*7$$!*[dgS)!#5$"+iVwNk!#57$$!+u/&pC#!#5$"+#4)o3%*!#57$$"*/JvW$!#5$"+W90%Q(!#57$$!*oH3>"!#5$"+'e#)H,(!#57$$"+aL%)GT!#5$"+$ouIq"!#5-%)POLYGONSG6'7&7$$"+D)\u3)!#5$"*s>*Rl!"*7$$"+v,b7z!#5$"*G!3gi!"*7$$"*rhh9#!"*$"+tI2k)*!#57$$"*Oh5K#!"*$"+^7R95!"*7%7$$"*MU8$=!"*$"+"3i.O*!#57$$!)/$)*z%!"*$"*%*)**p6!")7$$"*t!)ej#!"*$"*NiZ1"!")-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"+D)\u3)!#5$"*s>*Rl!"*7$$"+v,b7z!#5$"*G!3gi!"*7$$"*rhh9#!"*$"+tI2k)*!#57$$"*MU8$=!"*$"+"3i.O*!#57$$!)/$)*z%!"*$"*%*)**p6!")7$$"*t!)ej#!"*$"*NiZ1"!")7$$"*Oh5K#!"*$"+^7R95!"*7$$"+D)\u3)!#5$"*s>*Rl!"*-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%!z$!""-%.BOUNDS_HEIGHTG6#$"%?N!""-%)CHILDRENG6"

Figura 3 Vetores tangentes unit\303\241rios e vetores normais principais ao longo da par\303\241bola na Figura 2

No gr\303\241fico na Figura 2, Figura 4 sobrep\303\265e os vetores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSgmcHJpbWU7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRidGPg== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSgmUHJpbWU7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRjs2LVEiLkYnRj5GQEZCRkRGRkZIRkpGTC9GT0ZTRlFGPg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEzUGxvdFBvc2l0aW9uVmVjdG9yRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvRjdGSC8lKnVuZGVybGluZUdGSC8lKnN1YnNjcmlwdEdGSC8lLHN1cGVyc2NyaXB0R0ZILyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRkgvJStleGVjdXRhYmxlR0ZILyUpcmVhZG9ubHlHRkgvJSljb21wb3NlZEdGSC8lKmNvbnZlcnRlZEdGSC8lK2ltc2VsZWN0ZWRHRkgvJSxwbGFjZWhvbGRlckdGSC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGSC9GOlEnbm9ybWFsRicvJSZmZW5jZUdGSC8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZicC1JKG1mZW5jZWRHRiQ2JC1GIzYqLUYsNidRIlJGJy9GR0Y4RkkvRjpRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRl9xLUY9Ni1RIixGJ0Zgb0Ziby9GZW9GOEZmb0Zob0Zqb0ZccEZecEZgcC9GZHBRLDAuMzMzMzMzM2VtRictRiM2KC1GLDYlUSJ0RidGNkY5LUY9Ni1RIj1GJ0Zgb0Zib0Zkb0Zmb0Zob0Zqb0ZccEZecC9GYXBRLDAuMjc3Nzc3OGVtRicvRmRwRmFyLUYjNihGKy1GIzYmLUY9Ni1RKiZ1bWludXMwO0YnRmBvRmJvRmRvRmZvRmhvRmpvRlxwRl5wL0ZhcFEsMC4yMjIyMjIyZW1GJy9GZHBGW3MtSSNtbkdGJDYkUSIxRidGYG9GWEZgby1GPTYtUSMuLkYnRmBvRmJvRmRvRmZvRmhvRmpvRlxwRl5wRmpyRmNwRl1zRlhGYG9GK0ZYRmBvRmJxLUYjNictRiw2JVEncHZkaWZmRidGNkY5Rl1yLUZmcDYmLUYjNictRmZwNiYtRiM2JUZqcUZYRmBvRmBvLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmJxLUZmcDYmLUYjNidGanFGYnFGanFGWEZgb0Zgb0ZhdEZkdEZYRmBvRmBvRmF0RmR0RlhGYG9GK0ZYRmBvRmBvRlhGYG9GK0ZYRmBvRitGWEZgbw==

-%%PLOTG69-%'CURVESG6%7dw7$$!#5!""$"#5!""7$$!0\(\**y%[*)*!#:$"0)*=a\,3z*!#:7$$!0[&4>cN.)*!#:$"04X%R"y0h*!#:7$$!0_/4)HY+(*!#:$"0"**Q/#)*)4%*!#:7$$!0f<NI))of*!#:$"0F>5^E+@*!#:7$$!0Y#\)*e!Q\*!#:$"0.DQ/NK,*!#:7$$!0%yc8`B)R*!#:$"0O>4q#oK))!#:7$$!0rU&3vF*H*!#:$"0%))3=ilZ')!#:7$$!08D]?Np>*!#:$"00Vlrh$e%)!#:7$$!0'Gd96#\4*!#:$"0LI!3!f<F)!#:7$$!04<M3()**)*)!#:$"/1+wn)>3)!#97$$!0He;8hv*))!#:$"0kf"4%fm"z!#:7$$!0.05S6Nz)!#:$"0agfF%eKx!#:7$$!/3;KW.*o)!#9$"/wKO>$*\v!#97$$!0%yc8:N)e)!#:$"/.1s"yfP(!#97$$!0X*)yx@p\)!#:$"/s&*pzw>s!#97$$!0Z%*)yH?)Q)!#:$"0T8:#\>Oq!#:7$$!0Rxa*Q5'H)!#:$"0^bW)R`#)o!#:7$$!0<Mowq*)=)!#:$"0Y1?ACfq'!#:7$$!0)[(\zRT4)!#:$"0ff?!*4:b'!#:7$$!0sW*)=&4!*z!#:$"0wRG6iTQ'!#:7$$!0*zf>,-"*y!#:$"0.!z_)>oA'!#:7$$!0'>Ryck(y(!#:$"/x@@Dukg!#97$$!0yc8n:Fp(!#:$"0#Q.Suy<f!#:7$$!0&3<M3K!f(!#:$"0"[cOqHhd!#:7$$!/%zePhR[(!#9$"0Zlvyn4g&!#:7$$!0(Qxa^P"R(!#:$"0%3'ymUKY&!#:7$$!0\(\*\z8H(!#:$"0Ap0]@kJ&!#:7$$!03:I?u!)=(!#:$"030[2To;&!#:7$$!07BY75q3(!#:$"00^1DrD-&!#:7$$!/3;KaA*)p!#9$"0McT@F\)[!#:7$$!03:I?_1)o!#:$"0i&)QZPVt%!#:7$$!0>QwK%4$y'!#:$"0ujd'o.,Y!#:7$$!0"=Os/$*ym!#:$"0JkaA63Y%!#:7$$!0W)oPDa%e'!#:$"0'G1V+iNV!#:7$$!0&)pRf^8['!#:$"0bl%[=z+U!#:7$$!0&*)ydpD%Q'!#:$"0m2.pte2%!#:7$$!0;Kk3lFG'!#:$"04HJr8t%R!#:7$$!0yb6BQN='!#:$"0^;c]9O#Q!#:7$$!0uZ&4plzg!#:$"0;"y8GA'p$!#:7$$!0E^-&ogzf!#:$"0<d$3)pbd$!#:7$$!0NqS@"Hxe!#:$"0&))\,_DaM!#:7$$!02:I!G#ex&!#:$"0*G=0H,OL!#:7$$!0yc8(Qe#o&!#:$"0U+b%f<HK!#:7$$!0MoO`@dd&!#:$"0G,@1n)3J!#:7$$!0iC\eU,[&!#:$"0V5^F'>.I!#:7$$!0E_/\N#y`!#:$"0.w!*pTD*G!#:7$$!0&**)zR(p!G&!#:$"0y84]w&)y#!#:7$$!0.29)QRs^!#:$"0pTk%eOvE!#:7$$!0&)pR*4hy]!#:$"092G'*G#zD!#:7$$!0X*)ydm@(\!#:$"04Gy/WAZ#!#:7$$!0@T#[S:v[!#:$"0E3%*p7nP#!#:7$$!0nMpeP!pZ!#:$"0df0&>PuA!#:7$$!0oNr-xun%!#:$"/#QR8zy=#!#97$$!0$f=P-?tX!#:$"0uR4/;94#!#:7$$!0:Ig+uCZ%!#:$"0ahMP-.+#!#:7$$!0U%)od8=P%!#:$"/J5&Rv7">!#97$$!0['HfM_rU!#:$"0-KjE"fC=!#:7$$!0LmK0w^<%!#:$"0'od2&4Ku"!#:7$$!0*)yd&>-rS!#:$"0QVk(>Kd;!#:7$$!0sV([bvrR!#:$"0l(*Q@%[x:!#:7$$!0C['HBGnQ!#:$"0&4shse&\"!#:7$$!0rU&3*3Fx$!#:$"0wf3DLLU"!#:7$$!0NpQd(=oO!#:$"0&*3x+gbM"!#:7$$!0sV([V2oN!#:$"0H;eX:JF"!#:7$$!005?![?oM!#:$"0co[XWG?"!#:7$$!0$oOt1*QO$!#:$"0WOi/w:8"!#:7$$!0#Qw_N"yE$!#:$"0pi:agy1"!#:7$$!0)f>RuTpJ!#:$"0'zQ!p?X+"!#:7$$!0&4>QkxgI!#:$"/\e/CNo$*!#:7$$!0w_0"4TiH!#:$"01iHSyex)!#;7$$!0MoOt8='G!#:$"0t7i%y(**=)!#;7$$!/*zf**3&fF!#9$"0*R*))*)*)[h(!#;7$$!0&3<M5ZlE!#:$"0%Q+Met/r!#;7$$!/.17'H_c#!#9$"0/"fiHS!e'!#;7$$!0&3<M7vlC!#:$"04:)["H*zg!#;7$$!0Hd9HS$fB!#:$"0v$*3h'[mb!#;7$$!06@UCPaE#!#:$"07/v!f?K^!#;7$$!0`06i#4d@!#:$"0"z-w&[Il%!#;7$$!0ze<&*>$f?!#:$"0%=rj')zSU!#;7$$!0:Ig+zD'>!#:$"0H5\N;<&Q!#;7$$!0Gb5T^&e=!#:$"0cNvM8UX$!#;7$$!03:I+.Tv"!#:$"/l=Xt(o2$!#:7$$!0V&3</2f;!#:$"0,[)[Y^_F!#;7$$!/3;K+:e:!#9$"0rAF_JyU#!#;7$$!);mf9!")$"0c9l)>hI@!#;7$$!0^-05**GN"!#:$"0^Sh(fLI=!#;7$$!0Qw_&)>0E"!#:$"0*fa0."*)e"!#;7$$!0MoO$*=W:"!#:$"0&>TuIoK8!#;7$$!0CZ%*[yY0"!#:$"/F5;nM76!#:7$$!0Hd9H9!f&*!#;$"0ZGCUvu8*!#<7$$!0uZ&4zXq&)!#;$"0$H$z([FXt!#<7$$!0Pu[(H>iv!#;$"0$R#*ein=d!#<7$$!0)e<N!\M\'!#;$"0mUs.)[;U!#<7$$!0W([(\:N^&!#;$"0U.TJ&))RI!#<7$$!0nJjE&>YX!#;$"0kh*R"*ym?!#<7$$!0\'Hfe97N!#;$"0N(p`o^L7!#<7$$!0=Pu[Z.[#!#;$"0&fVeO7_h!#=7$$!0Rze<ZUb"!#;$"00HPG%o:C!#=7$$!0<V'Gd9sX!#<$".&Rc;X!4#!#<7$$"0Cf=P9tg%!#<$"029@dMF7#!#>7$$"0/5?SsV`"!#;$"02]!o')HaB!#=7$$"0LnMpe!fD!#;$"0s5mR"y[l!#=7$$"0V([(\")RZ$!#;$"/&)[WZ&o?"!#;7$$".(Rzy!H]%!#9$"0cLq$zhF?!#<7$$"0LmKla'Qb!#;$"0(["o`pw1$!#<7$$"0e<Nqy%pl!#;$"06(fV]!eJ%!#<7$$"0"Qw_X=Dv!#;$"/bJb-%Gm&!#;7$$"04:IgiZ^)!#;$"0Vq&=#=,D(!#<7$$"0&4>Qc=Q&*!#;$"0Afo_)p(4*!#<7$$"0OrUlKe0"!#:$"/d#Qf#y96!#:7$$"08Faom2;"!#:$"/v*zHztM"!#:7$$"0$f=PE>`7!#:$"0-(*ey"\q:!#;7$$"/#RyOUsN"!#9$"0vd]%o5U=!#;7$$"0U$oO$><Y"!#:$"0@M#>MiO@!#;7$$"0Qw_D-Cc"!#:$"0t#H235TC!#;7$$"0xa4*>$Ql"!#:$"0V0VDg^t#!#;7$$"0v\**y]Dw"!#:$"0[_rG&e1J!#;7$$"0$oOt)\Y&=!#:$"0hzF:E(RM!#;7$$"005?+$yh>!#:$"0dvpa#f[Q!#;7$$"0NpQ(Rhc?!#:$"0n9v.h'HU!#;7$$"/&**)z&e1;#!#9$"0J$*))\X%oY!#;7$$"0BY#\OtfA!#:$"0pNb;'R1^!#;7$$"0E_/43JO#!#:$"0$4;Z)zUe&!#;7$$"0W([(4Q!eC!#:$"0n*p)G^>/'!#;7$$"0PtY$HVgD!#:$"02gH"o"eb'!#;7$$"0$['HR#zmE!#:$"01vrm"y6r!#;7$$"0NqShy$fF!#:$"0$))yN.<9w!#;7$$"0tY$pUPfG!#:$"0;-A@@g<)!#;7$$"09HeczE'H!#:$"0d"y4-Zx()!#;7$$"06@UkVP1$!#:$"0A0v6DlQ*!#;7$$"0U$oO$G:;$!#:$"0@_OUh_***!#;7$$"0:Hec,,F$!#:$"0#Q3DkNp5!#:7$$"0.17WfwO$!#:$"0T%>6I6M6!#:7$$"0T#['HB=Z$!#:$"/)*>+dN07!#97$$"0yb6B6ic$!#:$"0;AXD'yr7!#:7$$"0Pu[<-%pO!#:$"0G(4K7XY8!#:7$$"0Gb5"o\mP!#:$"0'*oF#)\'=9!#:7$$"017Co))z'Q!#:$"0yEZkLh\"!#:7$$"0W)oPb@nR!#:$"0mZA"*zQd"!#:7$$"0['Hfo4rS!#:$"0PxP'HQd;!#:7$$"0(Hf=p9rT!#:$"0w[;mY)R<!#:7$$"0(QxaDYtU!#:$"0W02A[i#=!#:7$$"0:He'4$\P%!#:$"03xb4-S">!#:7$$"0W([(*)p"oW!#:$"0H"GBUX'*>!#:7$$"0)e<NA.vX!#:$"0%)*G&*>4$4#!#:7$$"/'>R=61n%!#9$"0[NJ)3Y"=#!#:7$$"0'>Ry#=Dx%!#:$"0ae<2$pxA!#:7$$"0Fa3Pc+([!#:$"0$)Hb!\urB!#:7$$"0=Pu))f$y\!#:$"0O%)or1%yC!#:7$$"0Pu[xU@2&!#:$"0.rGBjEd#!#:7$$"0xa4>(ey^!#:$"03K%Hlx"o#!#:7$$"0,.1s*fv_!#:$"0m-7C&>$y#!#:7$$"0b4>=;<Q&!#:$"0rii!pG'*G!#:7$$"0a3<uwKZ&!#:$"0xK"Hen&*H!#:7$$"0He;``vd&!#:$"0R^)R."46$!#:7$$"029Gwz#yc!#:$"0Qyk5'GCK!#:7$$"/)f>>S*yd!#9$"0%[Au\hRL!#:7$$"0uZ&4.Bze!#:$"0[qK!\`cM!#:7$$"0*yd:xdvf!#:$"06"\.HvqN!#:7$$"0LlI"=tzg!#:$"0')z=*QJ'p$!#:7$$"/05?#)**yh!#9$"0_+/!>+=Q!#:7$$"0)f>R9Z$G'!#:$"0;>FL,#[R!#:7$$"0^,.'[/yj!#:$"0&=+Cc%z1%!#:7$$"0([(\>mD['!#:$"/JAZkO-U!#97$$"/05?%zEe'!#9$"0Z"yMo;LV!#:7$$"0<Mo'*[Do'!#:$"0l8%pgklW!#:7$$"0Rxa4joy'!#:$"0Hvw1^hg%!#:7$$"//3;-%H)o!#9$"0p8=g'[PZ!#:7$$"0C['HjL")p!#:$"0kmZp0R([!#:7$$"0F`1Lx**3(!#:$"0s<\&yxE]!#:7$$"0Y"HeGM)=(!#:$"0)\$[IFs;&!#:7$$"0)e<N+%*)G(!#:$"0(*QOokGJ&!#:7$$"0KkGxW7R(!#:$"0UR#H*\IY&!#:7$$"0PtYt#G&[(!#:$"0#**zhd%Hg&!#:7$$"0#RycT_&e(!#:$"0C:Ln<Sv&!#:7$$"0PtY`-]o(!#:$"0h$z&REf!f!#:7$$"0$pQxMT"z(!#:$"0ogvR712'!#:7$$"07BY_;`)y!#:$"0W\$p;#y@'!#:7$$"/(Qx9hO*z!#9$"0r'[a=')*Q'!#:7$$"0V&3<QV"4)!#:$"0OF;7Ira'!#:7$$"029Gwu")=)!#:$"0`QYf?Yq'!#:7$$"0&*)ydB?#H)!#:$"01_U*>1wo!#:7$$"0:Hew]mR)!#:$"0#*H$3WP]q!#:7$$"0ze<N$o"\)!#:$"0v`Yho3@(!#:7$$"0U$oOPg#f)!#:$"0emv*QG$Q(!#:7$$"0AW)o@4"p)!#:$"0`M(3$3Nb(!#:7$$"0rT$oY&yz)!#:$"/i_wYASx!#97$$"0%yc8RB!*))!#:$"0<&z.fi.z!#:7$$"0)e<N[L'**)!#:$"/*fm//M4)!#97$$"0*pRz_2'4*!#:$"/d%)[&eQF)!#97$$"0\)pRB&[>*!#:$"0*e)[&4`a%)!#:7$$"0X*)y(zq$H*!#:$"/'Gyz+tj)!#97$$"0yc8ZMXR*!#:$"04^LzFd#))!#:7$$"0jE`')39]*!#:$"0v5E/xw-*!#:7$$"0[&4>AS*f*!#:$"0_(R'H_[@*!#:7$$"016ACMhp*!#:$"0y(HC>],%*!#:7$$"0d9H=R&*z*!#:$"/yu>o4.'*!#97$$"/05?!>F!**!#9$"0-1"*R%Q1)*!#:7$$"#5!""$"#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%)POLYGONSG6'7&7$$!*s>*R")!"*$"+v,b7j!#57$$!*G!3gy!"*$"+D)\u['!#57$$!*G!3g5!"*$!*=]DR%!"*7$$!*s>*R8!"*$!*$)\uc%!"*7%7$$!)Hpjb!"*$!)3txS!")7$$""#!""$!#'*!"#7$$!*rIO%=!"*$!)#pA)[!")-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$!*s>*R")!"*$"+v,b7j!#57$$!*G!3gy!"*$"+D)\u['!#57$$!*G!3g5!"*$!*=]DR%!"*7$$!)Hpjb!"*$!)3txS!")7$$""#!""$!#'*!"#7$$!*rIO%=!"*$!)#pA)[!")7$$!*s>*R8!"*$!*$)\uc%!"*7$$!*s>*R")!"*$"+v,b7j!#5-%)POLYGONSG6'7&7$$!+$ouI5%!#5$"+Ym:r9!#57$$!+<`#p*Q!#5$"+aL%)G<!#57$$"+$ouI!H!#5$!+Ym:6P!#57$$"+<`#pp#!#5$!+aL%)oR!#57%7$$"+TN9uK!#5$!+u0KZK!#57$$""'!""$!#k!"#7$$"+fk&eK#!#5$!+E%zEV%!#5-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$!+$ouI5%!#5$"+Ym:r9!#57$$!+<`#p*Q!#5$"+aL%)G<!#57$$"+$ouI!H!#5$!+Ym:6P!#57$$"+TN9uK!#5$!+u0KZK!#57$$""'!""$!#k!"#7$$"+fk&eK#!#5$!+E%zEV%!#57$$"+<`#pp#!#5$!+aL%)oR!#57$$!+$ouI5%!#5$"+Ym:r9!#5-%)POLYGONSG6'7&7$$""!!""$!$l"!"%7$$""!!""$"$l"!"%7$$"#o!"#$"$l"!"%7$$"#o!"#$!$l"!"%7%7$$"#o!"#$"$f(!"%7$$"#5!""$""!!""7$$"#o!"#$!$f(!"%-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$""!!""$!$l"!"%7$$""!!""$"$l"!"%7$$"#o!"#$"$l"!"%7$$"#o!"#$"$f(!"%7$$"#5!""$""!!""7$$"#o!"#$!$f(!"%7$$"#o!"#$!$l"!"%7$$""!!""$!$l"!"%-%)POLYGONSG6'7&7$$"+$ouI5%!#5$"+Ym:r9!#57$$"+<`#p*Q!#5$"+aL%)G<!#57$$"+KDpp5!"*$"+aL%)or!#57$$"+ouI!4"!"*$"+Ym:6p!#57%7$$"+YceK5!"*$"+E%zEj(!#57$$"#9!""$"#'*!"#7$$"+aVTF6!"*$"+u0KZk!#5-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"+$ouI5%!#5$"+Ym:r9!#57$$"+<`#p*Q!#5$"+aL%)G<!#57$$"+KDpp5!"*$"+aL%)or!#57$$"+YceK5!"*$"+E%zEj(!#57$$"#9!""$"#'*!"#7$$"+aVTF6!"*$"+u0KZk!#57$$"+ouI!4"!"*$"+Ym:6p!#57$$"+$ouI5%!#5$"+Ym:r9!#5-%)POLYGONSG6'7&7$$"*s>*R")!"*$"+v,b7j!#57$$"*G!3gy!"*$"+D)\u['!#57$$"+G!3gY"!"*$"+$)\uO<!"*7$$"+s>*R\"!"*$"+=]D><!"*7%7$$"+Hpj:9!"*$"*#pAo<!")7$$"#=!""$"$C#!"#7$$"+rIOW:!"*$"*3txo"!")-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"*s>*R")!"*$"+v,b7j!#57$$"*G!3gy!"*$"+D)\u['!#57$$"+G!3gY"!"*$"+$)\uO<!"*7$$"+Hpj:9!"*$"*#pAo<!")7$$"#=!""$"$C#!"#7$$"+rIOW:!"*$"*3txo"!")7$$"+s>*R\"!"*$"+=]D><!"*7$$"*s>*R")!"*$"+v,b7j!#5-%)POLYGONSG6'7&7$$!%Ny!"%$"#k!"#7$$!%l")!"%$"#k!"#7$$!%l")!"%$"#?!""7$$!%Ny!"%$"#?!""7%7$$!%f()!"%$"#?!""7$$!")!""$"$k#!"#7$$!%Ts!"%$"#?!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$!%Ny!"%$"#k!"#7$$!%l")!"%$"#k!"#7$$!%l")!"%$"#?!""7$$!%f()!"%$"#?!""7$$!")!""$"$k#!"#7$$!%Ts!"%$"#?!""7$$!%Ny!"%$"#?!""7$$!%Ny!"%$"#k!"#-%)POLYGONSG6'7&7$$!%NQ!"%$"#;!"#7$$!%lT!"%$"#;!"#7$$!%lT!"%$"$_"!"#7$$!%NQ!"%$"$_"!"#7%7$$!%fZ!"%$"$_"!"#7$$!"%!""$"$;#!"#7$$!%TK!"%$"$_"!"#-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$!%NQ!"%$"#;!"#7$$!%lT!"%$"#;!"#7$$!%lT!"%$"$_"!"#7$$!%fZ!"%$"$_"!"#7$$!"%!""$"$;#!"#7$$!%TK!"%$"$_"!"#7$$!%NQ!"%$"$_"!"#7$$!%NQ!"%$"#;!"#-%)POLYGONSG6'7&7$$"$l"!"%$""!!""7$$!$l"!"%$""!!""7$$!$l"!"%$"$O"!"#7$$"$l"!"%$"$O"!"#7%7$$!$f(!"%$"$O"!"#7$$""!!""$"#?!""7$$"$f(!"%$"$O"!"#-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"$l"!"%$""!!""7$$!$l"!"%$""!!""7$$!$l"!"%$"$O"!"#7$$!$f(!"%$"$O"!"#7$$""!!""$"#?!""7$$"$f(!"%$"$O"!"#7$$"$l"!"%$"$O"!"#7$$"$l"!"%$""!!""-%)POLYGONSG6'7&7$$"%lT!"%$"#;!"#7$$"%NQ!"%$"#;!"#7$$"%NQ!"%$"$_"!"#7$$"%lT!"%$"$_"!"#7%7$$"%TK!"%$"$_"!"#7$$""%!""$"$;#!"#7$$"%fZ!"%$"$_"!"#-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"%lT!"%$"#;!"#7$$"%NQ!"%$"#;!"#7$$"%NQ!"%$"$_"!"#7$$"%TK!"%$"$_"!"#7$$""%!""$"$;#!"#7$$"%fZ!"%$"$_"!"#7$$"%lT!"%$"$_"!"#7$$"%lT!"%$"#;!"#-%)POLYGONSG6'7&7$$"%l")!"%$"#k!"#7$$"%Ny!"%$"#k!"#7$$"%Ny!"%$"#?!""7$$"%l")!"%$"#?!""7%7$$"%Ts!"%$"#?!""7$$"")!""$"$k#!"#7$$"%f()!"%$"#?!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%*THICKNESSG6#"""-%&STYLEG6#%,PATCHNOGRIDG-%'CURVESG6#7*7$$"%l")!"%$"#k!"#7$$"%Ny!"%$"#k!"#7$$"%Ny!"%$"#?!""7$$"%Ts!"%$"#?!""7$$"")!""$"$k#!"#7$$"%f()!"%$"#?!""7$$"%l")!"%$"#?!""7$$"%l")!"%$"#k!"#-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%?Q!""-%.BOUNDS_HEIGHTG6#$"%!)Q!""-%)CHILDRENG6"

Figura 4 Vetores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSgmcHJpbWU7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRidGPg== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSgmUHJpbWU7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRidGPg== ao longo da par\303\241bola na Figura 2

O cardi\303\263ide 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 \303\251 capturado pelo PositionVector que \303\251 constru\303\255do atrav\303\251s de

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj4tSSNtb0dGJDYtUSM6PUYnL0Y9USdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlctRiM2Jy1GLDYlUS9Qb3NpdGlvblZlY3RvckYnL0Y6RjgvRj1RJ2l0YWxpY0YnLUZCNj5RMCZBcHBseUZ1bmN0aW9uO0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy9GN0Y7RjkvJSp1bmRlcmxpbmVHRjsvJSpzdWJzY3JpcHRHRjsvJSxzdXBlcnNjcmlwdEdGOy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y7LyUrZXhlY3V0YWJsZUdGOy8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjsvJSpjb252ZXJ0ZWRHRjsvJStpbXNlbGVjdGVkR0Y7LyUscGxhY2Vob2xkZXJHRjsvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjtGRUZHRklGS0ZNRk9GUUZTL0ZWUSYwLjBlbUYnL0ZZRmNxLUkobWZlbmNlZEdGJDYkLUYjNigtRmZxNiYtRiM2KEYrLUYjNigtSSNtbkdGJDYkUSIxRidGRS1GQjYtUSIrRidGRUZHRklGS0ZNRk9GUUZTL0ZWUSwwLjIyMjIyMjJlbUYnL0ZZRmhyLUYjNictRiw2JVEkY29zRidGOUZFRlxvLUZmcTYkLUYjNiUtRiw2JVEnJiM5NTI7RidGOUZFRmRwRkVGRUZkcEZFRitGZHBGRS1GQjYtUSIsRidGRUZHL0ZKRjhGS0ZNRk9GUUZTRmJxL0ZZUSwwLjMzMzMzMzNlbUYnRmNzRmRwRkVGRS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zmcy1GLDYlUSZwb2xhckYnRjlGRS1GZnE2Ji1GIzYnLUYsNiVRInJGJ0ZpbkZqbkZmc0Zjc0ZkcEZFRkVGXHRGX3RGZHBGRUZFRmRwRkVGK0ZkcEZFRitGZHBGRUYrRmRwRkU=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLUknUlRBQkxFR0YoNiUiKisjWyZbJS1JJ01BVFJJWEdGKDYjNyQ3IyomLCYiIiJGOS1JJGNvc0dGJTYjSSZ0aGV0YUdGKEY5RjlGOkY5NyMqJkY4RjktSSRzaW5HRiVGPEY5JkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZCNiMvSSQlaWRHRihGMQ==

O par\303\242metro de coordenadas no comando PositionVector indica o sistema de coordenadas no qual a representa\303\247\303\243o param\303\251trica deve ser interpretada. O vetor resultante \303\251 um vetor Cartesiano. A Figura 5 mostra um gr\303\241fico desta cardi\303\263ide.

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

-%%PLOTG6%-%'CURVESG6%7dw7$$"#?!""$""!!""7$$"/&z&GNO)*>!#8$"0pKGt(*Qg'!#;7$$"0kr;u!G%*>!#9$"0iHNe*eL7!#:7$$"0>X7]Yn)>!#9$"0&yA!)G6v=!#:7$$"0XR#\#Rg(>!#9$"0(o:\f%f^#!#:7$$"0)H5"R0B'>!#9$"0B%H.;9ZJ!#:7$$"0cY')3no%>!#9$"0ha(G[.DP!#:7$$"0Z\01%=G>!#9$"0HI)fuf9V!#:7$$"0/0W%>.1>!#9$"0>'4R[U8\!#:7$$"07M=<a6)=!#9$"0,wc(>#y\&!#:7$$"0H)4!HJF&=!#9$"0M"f*H)Q%3'!#:7$$"0j.Nt)QD=!#9$"/JE&*pg(e'!#97$$"/@*3-5@z"!#8$"0e4vldx8(!#:7$$"0E8OBNhv"!#9$"0-$pn*49n(!#:7$$"00cDnY"><!#9$"0(Q)4_lm;)!#:7$$"09t0zwOo"!#9$"0">-i4G*f)!#:7$$"0#RW$3#HR;!#9$"0E1$[FO"4*!#:7$$"0."HO=#**f"!#9$"03M+si$)[*!#:7$$"0W:nk:Ab"!#9$"0R(yR1FE**!#:7$$"0Z.`j$R3:!#9$"01NA$z;H5!#97$$"0#)***3-te9!#9$"0-w!>/ym5!#97$$"02kqGL+T"!#9$"/<^y">,5"!#87$$"0#f;b)3zN"!#9$"0*)fi!eEK6!#97$$"0D*f38**38!#9$"0"GY(ol$f6!#97$$"0'>F)eV_D"!#9$"07SNlbf="!#97$$"0O;kL'\)>"!#9$"0@U%)GN1@"!#97$$"/T@'Qq%[6!#8$"08KJoc'H7!#97$$"0$3hWa#R4"!#9$"0v1_$*4wC"!#97$$"0i(G)[kr."!#9$"/Yt-QKj7!#87$$"0Vd>%)RQ")*!#:$"0<\v@5fF"!#97$$"0U?!=B>t#*!#:$"/0>OLZ&G"!#87$$"0'Q![-eMn)!#:$".h+;)4$H"!#77$$"039[A=l8)!#:$"0W\/_)G(H"!#97$$"02SM%*onc(!#:$"0Vg&3)=!*H"!#97$$"03peI<\0(!#:$"0ahn%y<)H"!#97$$"0;*)y)o],l!#:$"0(*R2=)o%H"!#97$$"0(=ka#=z)f!#:$"0P([Xq+*G"!#97$$"0U3,!\sfa!#:$"/AG_![1G"!#87$$"0$z7LB1`\!#:$"/h#z?`,F"!#87$$"0R,e/">MW!#:$"0zs+<)yc7!#97$$"/LxJhwYR!#9$"09]!yAqT7!#97$$"/kXvh*=Y$!#9$"0x$e\B7C7!#97$$"0orj>Tc*H!#:$"06RmWPY?"!#97$$"0"4FnJ%3e#!#:$"0Vd$)*>-&="!#97$$"00i'*))=C7#!#:$"0BfbKP1;"!#97$$"0yM554&G<!#:$"0b)3x&3s8"!#97$$"0Be*>3+E8!#:$"0nCjGf16"!#97$$"0"*>bwmDe*!#;$"0-X1dTQ3"!#97$$"0QqCs+jq&!#;$"0&=uUqe_5!#97$$"0$puN[OID!#;$"0w@:R"QC5!#97$$!0D"p+%evm)!#<$"0h'>%)3=7**!#:7$$!0h$)[">RnP!#;$"0<EnL'\+'*!#:7$$!0"z_$yvRs'!#;$"04W:uT1D*!#:7$$!0Cm0V"*=4*!#;$"0%4:MkRU*)!#:7$$!0$H+6!4"e6!#:$"0OLF2Dae)!#:7$$!0&*\[CYvP"!#:$"/,L!p$*eB)!#97$$!/=:9zFw:!#9$"0cJB=LK)y!#:7$$!0,e0LtRv"!#:$"/X"e9j(Hv!#97$$!0@Z;p!z0>!#:$"06Qb&)H$*=(!#:7$$!01&z2"z$\?!#:$"02)4#y*e@o!#:7$$!0D!*\#>tm@!#:$"0`%Q$QDDZ'!#:7$$!0t!zpj9qA!#:$"0o#[(Gby5'!#:7$$!0rd'oZWYB!#:$".Ap@K6y&!#87$$!0:5WG.AT#!#:$"0xg%p;([U&!#:7$$!0lb^\KvX#!#:$"/v1oFR*3&!#97$$!/9Wg>@'[#!#9$"0b<=;(GhZ!#:7$$!."p.]I*\#!#8$"0D;t2@lU%!#:7$$!0e8pWgo\#!#:$"0ecF0hh7%!#:7$$!/lPXbr![#!#9$"0m8=o.s#Q!#:7$$!0pIZBDyW#!#:$"0$eb%4*33N!#:7$$!02;9eJ`S#!#:$"0$p#\X^(HK!#:7$$!0d/EmC.N#!#:$"0x\G=-h&H!#:7$$!0a$3A%*R$G#!#:$"0Ci5bY(*o#!#:7$$!0fO)RN+8A!#:$"0f`RkLfX#!#:7$$!0&3%R-d&H@!#:$"0iY$)fv'=A!#:7$$!/#*p08:R?!#9$"0%\V))ft&*>!#:7$$!0$*e")>5_$>!#:$"0x,*oQJr<!#:7$$!0_h6*yBQ=!#:$"0`M)3e[&e"!#:7$$!/QHEIR@<!#9$"0E;$RYS&Q"!#:7$$!0UT&puT7;!#:$"08(3ng.=7!#:7$$!0^t#p\D-:!#:$"0o`\@'pk5!#:7$$!0dL)e&QAQ"!#:$"0vaz2hG8*!#;7$$!0-jok*>h7!#:$"0%\i;2-^x!#;7$$!0*egqH_^6!#:$"0l#=!*3t6m!#;7$$!0%)Rg$HWO5!#:$"0`.\p0<_&!#;7$$!0fS-'\&QE*!#;$"0V*["[MKd%!#;7$$!09*[&4!f0")!#;$"0)ota`qoO!#;7$$!0\Wa[*4Sr!#;$"0D`n45_)H!#;7$$!0i\LNR;3'!#;$"0LM[T8xI#!#;7$$!0C/p2HL9&!#;$"0#*z^;0%p<!#;7$$!0%p)*\u3vU!#;$"0ekVopQK"!#;7$$!0rgpi$4tM!#;$"0dkeg*)Re*!#<7$$!0WvkP6*HF!#;$"/VMqlP5m!#;7$$!0R@Jb^0.#!#;$"0Dw9572?%!#<7$$!0Q$Hw\)RZ"!#;$"0-S]Fl*yD!#<7$$!0@H"e*>y+"!#;$"0r/8rl#\9!#<7$$!0nUY85S/'!#<$"0VB$*p$*fp'!#=7$$!0'Qjsx?DI!#<$"0N&zrw4iB!#=7$$!/u&R/N/>"!#;$"0%yx)y$H<e!#>7$$!01))GLs9."!#=$"0=*f$4!p"["!#?7$$!08+uc*RZ5!#=$!0nBE+Wh^"!#?7$$!0u!*GkD-;"!#<$!01zbEcqf&!#>7$$!0#yW]7_>K!#<$!0bju\JRf#!#=7$$!0d#)zj"G9f!#<$!0(f@e)*\!['!#=7$$!0QgY%QV*))*!#<$!0rr^h'R39!#<7$$!0Ywg/<s["!#;$!.&3!oBUh#!#:7$$!0#Gk]t<x?!#;$!03uytK*[V!#<7$$!0R]FhSTq#!#;$!0>'Gh(*p9l!#<7$$!/XQ$3>+V$!#:$!02L4)3d+%*!#<7$$!0vMeTyuD%!#;$!0[/.Ek`J"!#;7$$!0<kZ[XQ:&!#;$!0**zY=8^x"!#;7$$!07<>n&HVh!#;$!0nOA([8XB!#;7$$!0>d&z$y^1(!#;$!0M\vL)zMH!#;7$$!0Nypzz=:)!#;$!0BDPvmIq$!#;7$$!0Gy!4^c'G*!#;$!0FcvZ9>f%!#;7$$!0'z674DT5!#:$!07;'**4>lb!#;7$$!0%oWDm]X6!#:$!0DZm$Q9_l!#;7$$!0b@3@$)4F"!#:$!0"[/!y&pdy!#;7$$!06h.9?xP"!#:$!0P93Dn(y!*!#;7$$!0TiXUT8]"!#:$!0.Y"H[[j5!#:7$$!.`#*Qj$4;!#8$!/^v::e87!#97$$!0wOEm5`s"!#:$!0f&)=FX<R"!#:7$$!0LF_N4A$=!#:$!0*)R7rpXd"!#:7$$!0Q><#\+R>!#:$!0f__%)4!z<!#:7$$!0tG4oa=.#!#:$!0n(oMz(*y>!#:7$$!0B,VMj`7#!#:$!0)H;6xj2A!#:7$$!00-NmZS@#!#:$!0'3;sV9fC!#:7$$!0z1F]2LG#!#:$!0vH&))\T*o#!#:7$$!0[vVq`)[B!#:$!0LI=$)3'\H!#:7$$!0))pVEjaS#!#:$!/XQ2u\IK!#97$$!0")H68C*[C!#:$!0EcG%[k;N!#:7$$!04g)>s%)yC!#:$!0T.,nLO!Q!#:7$$!0r\:kuq\#!#:$!0)R5b&>K8%!#:7$$!0@oqSA"*\#!#:$!0*yTrRYQW!#:7$$!0VSAB`a[#!#:$!0$oMT10tZ!#:7$$!0@N%*e;#eC!#:$!0#=@U!4K3&!#:7$$!0#\t<'[:T#!#:$!0XK7Ty*Ga!#:7$$!0P6u%>*3N#!#:$!0.a7G1)fd!#:7$$!01H-?:&pA!#:$!0.C&z)3.6'!#:7$$!0)Q/g1lr@!#:$!0FC;/7mX'!#:7$$!03.&=MG\?!#:$!0)G"H&Q&=#o!#:7$$!0*f)pxR<">!#:$!0'pf<44vr!#:7$$!0M.;bG2v"!#:$!09!\%z4m`(!#:7$$!0Dn!*eI/d"!#:$!0Q+#pH>%*y!#:7$$!0HCJqjkQ"!#:$!0N.H?u3A)!#:7$$!0"G0Eo#R:"!#:$!08d=RV<f)!#:7$$!0e6(G3fi#*!#;$!/8sVE2>*)!#97$$!0KM#QXgIm!#;$!03%>9-Di#*!#:7$$!0#[3Qlg9R!#;$!0mi]-#*Qe*!#:7$$!0wJ+zq@v'!#<$!0o>"*e'yJ**!#:7$$"0&GB-lf<B!#;$!0V![O(*RA5!#97$$"/(*3bT)>#f!#:$!0QXnp8W0"!#97$$"0E4jZ$=&R*!#;$!0.['[US#3"!#97$$"0nI0'QWR8!#:$!00r#Q:f66!#97$$"0*QAzj"3q"!#:$!/X!RZpa8"!#87$$"/(ya.?,8#!#9$!0le"3=2h6!#97$$"/ySlF-iD!#9$!0M$Qy$yS="!#97$$"0$*=]!)R(4I!#:$!0$fbsaE07!#97$$"0f`%Q7&4Z$!#:$!0k<V:vWA"!#97$$"0>8]J0u#R!#:$!0JGj_]5C"!#97$$"0hS"Q1cMW!#:$!0u2@m)zc7!#97$$"0Q'oX)H,$\!#:$!0G$\4$>'p7!#97$$"0.GRbnLY&!#:$!/H5<Yr!G"!#87$$"0:G[-A`&f!#:$!0N-1"ec)G"!#97$$"/J4iz(z]'!#9$!0h/'[Yu%H"!#97$$"0zlOGk[/(!#:$!0Ww+[Q")H"!#97$$"0M(*=F$['e(!#:$!0P(=Md+*H"!#97$$"0'=_&))4s:)!#:$!0Zfz.trH"!#97$$"0vmDkygo)!#:$!0-l`xpHH"!#97$$"0BY#yZdH#*!#:$!06N:>LhG"!#97$$"0WRf)zBI)*!#:$!0a#o!*)zbF"!#97$$"0'HW1DJP5!#9$!02!ftmGj7!#97$$"0FpHG*e#4"!#9$!0UE&>U,[7!#97$$"0*Q$pe*R[6!#9$!0V8a%=oH7!#97$$"0P<BQ1#*>"!#9$!0Ek")=Z.@"!#97$$"0c1)\Kq_7!#9$!04CPVLr="!#97$$"0W^wQw\I"!#9$!0vpjck9;"!#97$$"0i#\?0$)f8!#9$!0$)*=(4U68"!#97$$"0$Rj'*4>29!#9$!0`M>hj>5"!#97$$"0GR_?e/Y"!#9$!0NhH.Nb1"!#97$$"0"QJ#RAr]"!#9$!0$3d9$z,."!#97$$"0U!)['Q&=b"!#9$!0)[$\rD%H**!#:7$$"-(=r>#)f"!#6$!0=-hvmZ]*!#:7$$"0AwsqBGk"!#9$!0%)RkqAS0*!#:7$$"/a2$=#f"o"!#8$!0<p>IcNi)!#:7$$"0@>0Y`2s"!#9$!0C(Hn<9Y")!#:7$$"0xx\#y'ov"!#9$!0^cSJ*3hw!#:7$$"0'p-$y]Nz"!#9$!0V(3Pm::r!#:7$$"/Q&[vIJ#=!#8$!0<^/RIpi'!#:7$$"0nvGpIX&=!#9$!0Glji_$\g!#:7$$"0rDh(4X")=!#9$!0b-q\&G"\&!#:7$$"0"yS#o^b!>!#9$!0"=(*Hm[D\!#:7$$"0xA$4?0F>!#9$!0Uyn]%[ZV!#:7$$"0s6pZ<i%>!#9$!/GthKDZP!#97$$"0L>'GBUj>!#9$!0&3;2y%35$!#:7$$"0ey&*)fLw>!#9$!/yC0QY+D!#97$$"0*3b[:O')>!#9$!0@:qZ1?!>!#:7$$"0s>L"o0%*>!#9$!.r4W_uD"!#87$$"0/#)*)H*f)*>!#9$!0n#z"ol*4h!#;7$$"#?!""$"0lA"Gu#3k"!#B-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""#-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"#!*!""-%)BOUNDS_YG6#$"#q!""-%-BOUNDS_WIDTHG6#$"%IQ!""-%.BOUNDS_HEIGHTG6#$"%]Q!""-%)CHILDRENG6"

Figure 5 Cardi\303\263ide 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 capturado como um VetorPosi\303\247\303\243o

<Text-field style="Heading 3" layout="Heading 3">RootedVector</Text-field>

Em um espa\303\247o Cartesiano, a transla\303\247\303\243o paralela de vetores \303\251 tomada como verdade. Por exemplo, o vetor 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 na verdade, tem sua extremidade na origem, e sua ponta no ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJiRidGNEY3Rj5GPkY+. Este vetor pode sempre ser pensado como a mesma seta com sua extremidade em um ponto arbitr\303\241rio no plano Cartesiano. Em coordenadas n\303\243o Cartesianas, perdemos a constru\303\247\303\243o do vetor posi\303\247\303\243o emanando da origem. Vetores s\303\243o setas com suas extremidades em diferentes pontos no espa\303\247o Cartesiano subjacente, mas s\303\243o expressos em termos dos vetores de base curvil\303\255nea que muda de ponto a ponto.

A constru\303\247\303\243o do Maple para "ligar" um vetor para um ponto \303\251 o RootedVector. O vetor

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2J1EiVkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj4tSSNtb0dGJDYtUSM6PUYnL0Y9USdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlctRiM2Jy1GLDYlUS1Sb290ZWRWZWN0b3JGJy9GOkY4L0Y9USdpdGFsaWNGJy1GQjY+UTAmQXBwbHlGdW5jdGlvbjtGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvRjdGO0Y5LyUqdW5kZXJsaW5lR0Y7LyUqc3Vic2NyaXB0R0Y7LyUsc3VwZXJzY3JpcHRHRjsvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGOy8lK2V4ZWN1dGFibGVHRjsvJSlyZWFkb25seUdGOy8lKWNvbXBvc2VkR0Y7LyUqY29udmVydGVkR0Y7LyUraW1zZWxlY3RlZEdGOy8lLHBsYWNlaG9sZGVyR0Y7LyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0Y7RkVGR0ZJRktGTUZPRlFGUy9GVlEmMC4wZW1GJy9GWUZjcS1JKG1mZW5jZWRHRiQ2JC1GIzYoRistRiM2Jy1GLDYlUSVyb290RidGaW5Gam4tRkI2LVEiPUYnRkVGR0ZJRktGTUZPRlFGU0ZVRlgtRmZxNiYtRiM2Jy1JI21uR0YkNiRRIjFGJ0ZFLUZCNi1RIixGJ0ZFRkcvRkpGOEZLRk1GT0ZRRlNGYnEvRllRLDAuMzMzMzMzM2VtRictRmdyNiRRIjJGJ0ZFRmRwRkVGRS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZkcEZFRmpyLUZmcTYmLUYjNihGKy1GIzYmLUZCNi1RKiZ1bWludXMwO0YnRkVGR0ZJRktGTUZPRlFGUy9GVlEsMC4yMjIyMjIyZW1GJy9GWUZjdEZmckZkcEZFRmpyRmZyRmRwRkVGRUZjc0Zmc0ZkcEZFRkVGZHBGRUYrRmRwRkVGK0ZkcEZFRitGZHBGRQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLUknUlRBQkxFR0YoNiUiKkt5NygpKS1JJ01BVFJJWEdGKDYjNyQ3IyEiIjcjIiIiJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY6NiMvSSQlaWRHRihGMQ==

est\303\241 ligado ao ponto de raiz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGNEY0RjdGNA==como verificamos na Figura 6.

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

Figura 6 O vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiakYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSgmbWludXM7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGUC1GLDYnUSJpRidGL0YyRjVGOEY+ transladado ao ponto de raiz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGNEY0RjQ=

Observe que o RootedVector \303\251 sempre apresentado como um vetor coluna, e \303\251 do tipo RootedVector, como vemos a partir de

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqUyMpNCgpKS1JJ01BVFJJWEdGKDYjNyY3JEknVHlwZTp+R0YoSS5Sb290ZWR+VmVjdG9yR0YoNyRJLUNvbXBvbmVudHM6fkdGKDckISIiIiIiNyRJLkNvb3JkaW5hdGVzOn5HRihJKmNhcnRlc2lhbkdGKDckSS1Sb290flBvaW50On5HRig3JEY7IiIjSSdNYXRyaXhHRiU3Iy1GQzYjL0kkJWlkR0YoRi8=

Uma seta de comprimento um e apontando na dire\303\247\303\243o radial de coordenadas polares \303\251 ligado ao ponto polar 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 com a seguinte sintaxe.

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJXR0YoLUknUlRBQkxFR0YoNiUiKkNpMCgpKS1JJ01BVFJJWEdGKDYjNyQ3IyIiIjcjIiIhJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY6NiMvSSQlaWRHRihGMQ==

Figura 7 verifica que o vetor W, desenhado no plano Cartesiano, \303\251 o vetor polar correto.

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

LSUlUExPVEc2Jy0lKVBPTFlHT05TRzYlNyY3JCQiK15qXTtfISM1JCIqL2FfYCkhIio3JCQiK1xPXCR5JSEjNSQiKi9hX3kpISIqNyQkIitcT1wkeSkhIzUkIitGZE1yOiEiKjckJCIrXmpdOyMqISM1JCIrRmRNWTohIio3JTckJCIrKUgoKXBjKSEjNSQiK0ZkJVFlIiEiKjckJCIjNSEiIiQiKzMzMEs8ISIqNyQkIistRixMJSohIzUkIitGZCVRYCIhIiotJSZTVFlMRUc2IyUsUEFUQ0hOT0dSSURHLSUnQ1VSVkVTRzYjNyo3JCQiK15qXTtfISM1JCIqL2FfYCkhIio3JCQiK1xPXCR5JSEjNSQiKi9hX3kpISIqNyQkIitcT1wkeSkhIzUkIitGZE1yOiEiKjckJCIrKUgoKXBjKSEjNSQiK0ZkJVFlIiEiKjckJCIjNSEiIiQiKzMzMEs8ISIqNyQkIistRixMJSohIzUkIitGZCVRYCIhIio3JCQiK15qXTsjKiEjNSQiK0ZkTVk6ISIqNyQkIiteal07XyEjNSQiKi9hX2ApISIqLSUlVklFV0c2JDskIiIhISIiJCIjNSEiIjskIiIhISIiJCIjPyEiIi0lKFNDQUxJTkdHNiMlLENPTlNUUkFJTkVERy0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJSs2ISIiLSUpQk9VTkRTX1lHNiMkIiQ/IiEiIi0lLUJPVU5EU19XSURUSEc2IyQiJSs9ISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJSFmJCEiIi0lKUNISUxEUkVORzYi

Figura 7 Vetor radial unit\303\241rio ligado ao ponto 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

mas desenhado no plano Cartesiano subjacente

Para outro exemplo de um RootedVector em coordenadas polares, altere as coordenadas no vetor 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 para obter

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWcEdGKC1JJ1JUQUJMRUdGKDYlIipzVVwoKiktSSdNQVRSSVhHRig2IzckNyMsJComIyIiIiIiJkY6KUY7I0Y6IiIjRjpGOjcjLCQqJiMiIiRGO0Y6RjxGOkY6JkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZENiMvSSQlaWRHRihGMQ==

Seu ponto de raiz 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 torna-se o ponto de raiz 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 verificamos com

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEmQWJvdXRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDY+UTAmQXBwbHlGdW5jdGlvbjtGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvJSVib2xkR1EmZmFsc2VGJy9GN0ZILyUqdW5kZXJsaW5lR0ZILyUqc3Vic2NyaXB0R0ZILyUsc3VwZXJzY3JpcHRHRkgvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGSC8lK2V4ZWN1dGFibGVHRkgvJSlyZWFkb25seUdGSC8lKWNvbXBvc2VkR0ZILyUqY29udmVydGVkR0ZILyUraW1zZWxlY3RlZEdGSC8lLHBsYWNlaG9sZGVyR0ZILyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0ZIL0Y6USdub3JtYWxGJy8lJmZlbmNlR0ZILyUqc2VwYXJhdG9yR0ZILyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmJwLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2J1EjVnBGJy9GR0Y4RkkvRjpRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRl9xRlhGYG9GYG9GWEZgb0YrRlhGYG9GK0ZYRmBv

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqO3daKCopLUknTUFUUklYR0YoNiM3JjckSSdUeXBlOn5HRihJLlJvb3RlZH5WZWN0b3JHRig3JEktQ29tcG9uZW50czp+R0YoNyQsJComIyIiIiIiJkY9KUY+I0Y9IiIjRj1GPSwkKiYjIiIkRj5GPUY/Rj1GPTckSS5Db29yZGluYXRlczp+R0YoJkkmcG9sYXJHRic2JEkickdGKEkmdGhldGFHRig3JEktUm9vdH5Qb2ludDp+R0YoNyQqJEY/Rj0tSSdhcmN0YW5HRiU2I0ZBSSdNYXRyaXhHRiU3Iy1GVDYjL0kkJWlkR0YoRi8=

Os componentes s\303\243o em rela\303\247\303\243o aos vetores de base unit\303\241rios (tangente \303\240 curva de coordenadas) no ponto de raiz. Figura 8 fornece evid\303\252ncia gr\303\241fica de que o vetor transformado determina a mesma seta, como visto na Figura 6.

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

Figura 8 O vetor 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 transformado para coordenadas polares

Os c\303\241lculos conducentes \303\240 Figura 8 pode ser verificados da seguinte forma. Primeiro, defina as linhas de coordenadas curvil\303\255neas de coordenadas polares pelo PositionVector

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY+LUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUC1GLDYlUSJ4RicvRjNGMS9GNlEnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJyRidGVkZXLUY7Ni1RIixGJ0Y+RkAvRkNGMUZERkZGSEZKRkwvRk9RJjAuMGVtRicvRlJRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NTI7RidGMkY+Rj5GPi1GOzYtUSJ+RidGPkZARkJGREZGRkhGSkZMRl9vL0ZSRmBvLUYsNidRImlGJ0YvRjJGNUY4LUY7Ni1RIitGJ0Y+RkBGQkZERkZGSEZKRkwvRk9RLDAuMjIyMjIyMmVtRicvRlJGYXAtRiw2JVEieUYnRlZGV0ZZRmZvLUYsNidRImpGJ0YvRjJGNUY4RmZvRjpGZm9GaG5GZm8tRiw2JVEkY29zRidGMkY+LUZaNiQtRiM2JEZjb0Y+Rj5GZm9Gam9GXXBGaG5GZm8tRiw2JVEkc2luRidGMkY+RlxxRmZvRmZwRj4=

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLUknUlRBQkxFR0YoNiUiKktrNnopLUknTUFUUklYR0YoNiM3JDcjKiZJInJHRigiIiItSSRjb3NHRiU2I0kmdGhldGFHRihGOTcjKiZGOEY5LUkkc2luR0YlRjxGOSZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GQjYjL0kkJWlkR0YoRjE=

Vetores tangentes unit\303\241rios ao longo da curva de coordenadas s\303\243o dadas por

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSJyRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0Y2USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVLUkobWFjdGlvbkdGJDYlLUkobWZlbmNlZEdGJDYoLUYjNiYtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYmLUkkbXRkR0YkNigtRiM2KC1GLzYlUSRjb3NGJy9GM0ZGRkItRj82PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdGRkZoby8lKnVuZGVybGluZUdGRi8lKnN1YnNjcmlwdEdGRi8lLHN1cGVyc2NyaXB0R0ZGLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRkYvJStleGVjdXRhYmxlR0ZGLyUpcmVhZG9ubHlHRkYvJSljb21wb3NlZEdGRi8lKmNvbnZlcnRlZEdGRi8lK2ltc2VsZWN0ZWRHRkYvJSxwbGFjZWhvbGRlckdGRi8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGRkZCRkRGR0ZJRktGTUZPRlEvRlRRJjAuMGVtRicvRldGYXItRmZuNiQtRiM2Ji1GLzYlUScmIzk1MjtGJ0Zob0ZCRmpwRmRxRkJGQkZqcEZkcUZCLyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0Zccy8lK2dyb3VwYWxpZ25HRlxzLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRmNzRmpyRl1zRl9zLUZebzYmLUZhbzYoLUYjNigtRi82JVEkc2luRidGaG9GQkZpb0ZjckZqcEZkcUZCRmpyRl1zRl9zRmFzRmRzRmpyRl1zRl9zLyUmYWxpZ25HUSVheGlzRicvRltzUSliYXNlbGluZUYnL0Zec1EnY2VudGVyRicvRmBzUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGNC8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRlx1LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmd1LyUmZnJhbWVHRmd1LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGRi8lLWVxdWFsY29sdW1uc0dGRi8lLWRpc3BsYXlzdHlsZUdGRi8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZkdUZqcEZkcUZCRkIvSSttc2VtYW50aWNzR0YkUSpDb2xWZWN0b3JGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zqdi8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjg4NzI2NTk2OEYnRkI=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiZUdGKDYjSSZ0aGV0YUdGKC1JJ1JUQUJMRUdGKDYlIipDXTE4Ki1JJ01BVFJJWEdGKDYjNyQ3IywkLUkkc2luR0YlRi8hIiI3Iy1JJGNvc0dGJUYvJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZBNiMvSSQlaWRHRihGNA==

Avalie esses vetores de base no ponto 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 para obter

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIjLUknUlRBQkxFR0YoNiUiKiN6ayIqKiktSSdNQVRSSVhHRig2IzckNyMsJComI0YwIiImIiIiKUY9I0Y+RjBGPiEiIjcjLCQqJiNGPkY9Rj5GP0Y+Rj4mSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRkY2Iy9JJCVpZEdGKEY0

As componentes do vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiVkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUSJwRicvRjZGNC9GOVEnaXRhbGljRicvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRQ== s\303\243o os coeficientes da combina\303\247\303\243o linear

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqJzRtdSIqLUknTUFUUklYR0YoNiM3JDcjISIiNyMiIiImSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRjg2Iy9JJCVpZEdGKEYv

Assim, n\303\263s recuperamos o vetor 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.

<Text-field style="Heading 3" layout="Heading 3">VectorField</Text-field>

Um campo vetorial \303\251 uma fun\303\247\303\243o F de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1GLzYlUSJuRicvRjNRJXRydWVGJy9GNlEnaXRhbGljRidGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGNQ== para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1GLzYlUSJuRicvRjNRJXRydWVGJy9GNlEnaXRhbGljRidGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGNQ==. Esta fun\303\247\303\243o \303\251 as vezes descrita como uma fun\303\247\303\243o vectorial de um argumento de vetor, e \303\251 denotado por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiRkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYnUSJ4RidGL0YyRjVGOC9GNlEnbm9ybWFsRidGQkZC. Em termos mais simples, o campo vetorial fornece uma receita para ligar uma seta para cada ponto em uma regi\303\243o de LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJnJlYWxzO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtRiw2JVEibkYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYn. Maple fornece a constru\303\247\303\243o do CampoVetorial, exemplificado atrav\303\251s de

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJGR0YoLUknUlRBQkxFR0YoNiUiKishPnUiKi1JJ01BVFJJWEdGKDYlNyQ3IyomSSJ4R0YoIiIiSSJ5R0YoRjk3IywmRjhGOUY6Rjk3JFEieEYoUSJ5RihRJmZpZWxkRigmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRkE2Iy9JJCVpZEdGKEYx

A exibi\303\247\303\243o padr\303\243o (com BasisFormat definido como true) inclui os vetores de base m\303\263veis, aqui, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRImVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GMjYlUSJfRidGNUY4L0Y5USdub3JtYWxGJy8lJ2FjY2VudEdGNy1GIzYkLUYyNiVRInhGJ0Y1RjhGQC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkA= e LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRImVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSVtcm93R0YkNiQtRi82JVEiX0YnRjJGNS9GNlEnbm9ybWFsRicvJSdhY2NlbnRHRjQtRjk2JC1GLzYlUSJ5RidGMkY1Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==. Em coordenadas Cartesianas, estes vetores s\303\243o nada mais do que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. No entanto, h\303\241 uma diferen\303\247a fundamental entre esses vetores com barra, e o "vetores de base" sem barra utilizados na exibi\303\247\303\243o de um vetor livre. Mais uma vez, gostar\303\255amos de lembrar que o vetor livre \303\251 apenas a nota\303\247\303\243o para um ponto, e \303\251 equivalente a uma seta s\303\263 em coordenadas Cartesianas. Em coordenadas n\303\243o Cartesianas, o "vetor de base" sem barra do vetor livre \303\251 apenas a nota\303\247\303\243o para um ponto.

Os vetores de base com barra do VectorField s\303\243o os vetores de base (unit\303\241rios) m\303\263veis em ambas as coordenadas Cartesianas e n\303\243o Cartesianas. Conceitualmente, s\303\243o fun\303\247\303\265es de posi\303\247\303\243o, mas no Maple leva a constru\303\247\303\243o do RootedVector para expressar a depend\303\252ncia posicional de qualquer vetor.

Se definirmos

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEsQmFzaXNGb3JtYXRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSZmYWxzZUYnRi9GMi9GM1Enbm9ybWFsRidGPS1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHRjwvJSpzZXBhcmF0b3JHRjwvJSlzdHJldGNoeUdGPC8lKnN5bW1ldHJpY0dGPC8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y8LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy8lK2V4ZWN1dGFibGVHRjxGPQ==

o campo vetorial F ser\303\241 exibido como um vetor coluna, como vemos em

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYnUSJGRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPC8lK2V4ZWN1dGFibGVHRjkvRjtRJ25vcm1hbEYnRitGP0ZB

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqKyE+dSIqLUknTUFUUklYR0YoNiM3JDcjKiZJInhHRigiIiJJInlHRihGNzcjLCZGNkY3RjhGNyZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GOzYjL0kkJWlkR0YoRi8=

O CampoVetorial carrega como atributo, tanto "vectorfield" e seu sistema de coordenadas, como vemos com

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

Vector[column](2, {1 = x*y, 2 = x+y}, datatype = anything, storage = rectangular, order = Fortran_order, attributes = [vectorfield, coords = cartesian[x, y]], shape = [])

O comando MapToBasis aplica a lei de transforma\303\247\303\243o contravariante para um VectorField, corretamente transformando os vetores no campo de um sistema de coordenadas para outro. Por exemplo, se o campo F \303\251 transformado em coordenadas polares, obter\303\255amos

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJHR0YoLUknUlRBQkxFR0YoNiUiKj86bicqKS1JJ01BVFJJWEdGKDYjNyQ3IyooLUkkc2luR0YlNiNJJnRoZXRhR0YoIiIiSSJyR0YoRjwsKComRj1GPCktSSRjb3NHRiVGOiIiI0Y8RjxGQUY8RjhGPEY8NyMqKCwqRkFGPEY4RjxGPSEiIkY/RjxGPEY9RjxGQUY8JkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZINiMvSSQlaWRHRihGMQ==

Quando o campo \303\251 exibido como um vetor coluna, os vetores de base LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRImVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GMjYlUSJfRidGNUY4L0Y5USdub3JtYWxGJy8lJ2FjY2VudEdGNy1GIzYkLUYyNiVRInJGJ0Y1RjhGQC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkA= e LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRImVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSVtcm93R0YkNiQtRi82JVEiX0YnRjJGNS9GNlEnbm9ybWFsRicvJSdhY2NlbnRHRjQtRjk2JC1GLzYlUScmIzk1MjtGJy9GM1EmZmFsc2VGJ0Y+Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== devem ser inferidos. Eles podem ser tornados vis\303\255veis pela

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYnUSJHRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPEY0LyUrZXhlY3V0YWJsZUdGOUY6Rj1GK0Y0Rj9GOkY9

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqPzpuJyopLUknTUFUUklYR0YoNiU3JDcjKigtSSRzaW5HRiU2I0kmdGhldGFHRigiIiJJInJHRihGOiwoKiZGO0Y6KS1JJGNvc0dGJUY4IiIjRjpGOkY/RjpGNkY6Rjo3IyooLCpGP0Y6RjZGOkY7ISIiRj1GOkY6RjtGOkY/Rjo3JFEickYoUSZ0aGV0YUYoUSZmaWVsZEYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZKNiMvSSQlaWRHRihGLw==

Avalia\303\247\303\243o dos resultados do VectorField em um RootedVector, com o ponto de avalia\303\247\303\243o tornando o ponto de raiz. Por exemplo, ter\303\255amos

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2J1EjRzFGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y+LUkjbW9HRiQ2LVEjOj1GJy9GPVEnbm9ybWFsRicvJSZmZW5jZUdGOy8lKnNlcGFyYXRvckdGOy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXLUYjNictRiw2JVEnZXZhbFZGRicvRjpGOC9GPVEnaXRhbGljRictRkI2PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnL0Y3RjtGOS8lKnVuZGVybGluZUdGOy8lKnN1YnNjcmlwdEdGOy8lLHN1cGVyc2NyaXB0R0Y7LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRjsvJStleGVjdXRhYmxlR0Y7LyUpcmVhZG9ubHlHRjsvJSljb21wb3NlZEdGOy8lKmNvbnZlcnRlZEdGOy8lK2ltc2VsZWN0ZWRHRjsvJSxwbGFjZWhvbGRlckdGOy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGO0ZFRkdGSUZLRk1GT0ZRRlMvRlZRJjAuMGVtRicvRllGY3EtSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYnUSJHRidGNkY5RjxGPy1GQjYtUSIsRidGRUZHL0ZKRjhGS0ZNRk9GUUZTRmJxL0ZZUSwwLjMzMzMzMzNlbUYnLUZmcTYmLUYjNigtSSNtbkdGJDYkUSIyRidGRUZdci1GIzYlLUZocjYkUSIzRidGRUZkcEZFRitGZHBGRUZFLyUlb3BlbkdRMyZMZWZ0QW5nbGVCcmFja2V0O0YnLyUmY2xvc2VHUTQmUmlnaHRBbmdsZUJyYWNrZXQ7RidGZHBGRUZFRmRwRkVGK0ZkcEZFRitGZHBGRUYrRmRwRkU=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHMUdGKC1JJ1JUQUJMRUdGKDYlIipvRCkpPiotSSdNQVRSSVhHRig2IzckNyMsJComIyIjRiIjOCIiIilGOyNGPCIiI0Y8Rjw3IywkKiYjIiIpRjtGPEY9RjwhIiImSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRkY2Iy9JJCVpZEdGKEYx

O vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiR0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1JI21uR0YkNiRRIjFGJy9GOVEnbm9ybWFsRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkM= \303\251 um RootedVector, como vemos em

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqIVtoJW8lLUknTUFUUklYR0YoNiM3JjckSSdUeXBlOn5HRihJLlJvb3RlZH5WZWN0b3JHRig3JEktQ29tcG9uZW50czp+R0YoNyQsJComIyIjRiIjOCIiIilGPiNGPyIiI0Y/Rj8sJComIyIiKUY+Rj9GQEY/ISIiNyRJLkNvb3JkaW5hdGVzOn5HRigmSSZwb2xhckdGJzYkSSJyR0YoSSZ0aGV0YUdGKDckSS1Sb290flBvaW50On5HRig3JCokRkBGPy1JJ2FyY3RhbkdGJTYjIyIiJEZCSSdNYXRyaXhHRiU3Iy1GWDYjL0kkJWlkR0YoRi8=

Os componentes s\303\243o os coeficientes dos vetores de base movendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRImVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1GMjYlUSJfRidGNUY4L0Y5USdub3JtYWxGJy8lJ2FjY2VudEdGNy1GIzYkLUYyNiVRInJGJ0Y1RjhGQC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkA= e LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRImVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSVtcm93R0YkNiQtRi82JVEiX0YnRjJGNS9GNlEnbm9ybWFsRicvJSdhY2NlbnRHRjQtRjk2JC1GLzYlUScmIzk1MjtGJy9GM1EmZmFsc2VGJ0Y+Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== avaliado no ponto de raiz 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 a representa\303\247\303\243o polar do ponto Cartesiano 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. O comando evalVF usa a nota\303\247\303\243o do vetor livre para o ponto de avalia\303\247\303\243o, e este ponto \303\251 interpretado no sistema de coordenadas ambiente

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

SSpjYXJ0ZXNpYW5HNiI=

O sistema de coordenadas ambiente pode ser definido com

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

JkkmcG9sYXJHSShfc3lzbGliRzYiNiRJInJHRiVJJnRoZXRhR0Yl

caso em que ter\303\255amos obtido

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNHMkdGKC1JJ1JUQUJMRUdGKDYlIiohKVFZbyUtSSdNQVRSSVhHRig2IzckNyMsJCooIiIjIiIiLUkkc2luR0YlNiMiIiRGOiwoKiZGOUY6KS1JJGNvc0dGJUY9RjlGOkY6RkJGOkY7RjpGOkY6NyMsJCooRjlGOiwqRkJGOkY7RjpGOSEiIkZARjpGOkZCRjpGOiZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GSTYjL0kkJWlkR0YoRjE=

O ponto de raiz para o vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiR0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkM= \303\251 dado por

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqZ25ZbyUtSSdNQVRSSVhHRig2IzcmNyRJJ1R5cGU6fkdGKEkuUm9vdGVkflZlY3RvckdGKDckSS1Db21wb25lbnRzOn5HRig3JCwkKigiIiMiIiItSSRzaW5HRiU2IyIiJEY9LCgqJkY8Rj0pLUkkY29zR0YlRkBGPEY9Rj1GRUY9Rj5GPUY9Rj0sJCooRjxGPSwqRkVGPUY+Rj1GPCEiIkZDRj1GPUZFRj1GPTckSS5Db29yZGluYXRlczp+R0YoJkkmcG9sYXJHRic2JEkickdGKEkmdGhldGFHRig3JEktUm9vdH5Qb2ludDp+R0YoNyRGPEZBSSdNYXRyaXhHRiU3Iy1GVTYjL0kkJWlkR0YoRi8=

de modo que \303\251 agora 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

<Text-field style="Heading 2" layout="Heading 2">Operadores Diferenciais</Text-field>

Os operadores diferenciais Divergence e Curl agem noVectorField, o primeiro retornando um campo escalar; o segundo, um VectorField. O operador diferencial Gradient atua em um campo escalar e retorna um VectorField, enquanto o operador Laplacian mapea um campo escalar para um campo escalar.

Embora exista uma estrutura de dados especial para o campo vetorial, n\303\243o existe estrutura fornecida para o campo escalar. Estes s\303\243o como alternativa dados por express\303\265es ordin\303\241ria do Maple, e como tal, n\303\243o pode conter o atributo de sistema de coordenadas.

Estamos pr\303\263ximos de dar exemplos do comportamento dos quatro operadores diferenciais de c\303\241lculo vetorial, usando o campo

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

Error, (in VectorCalculus:-Vector[column]) Vector has incorrect dimension for polar coordinates: try changing the current coordinate system

O Erro pode ser explicado da seguinte maneira. Lembre-se que anteriormente, o sistema de coordenadas ambiente foi definido para polar, como vemos em

JkkmcG9sYXJHSShfc3lzbGliRzYiNiRJInJHRiVJJnRoZXRhR0Yl

Existem ent\303\243o duas op\303\247\303\265es: usar o comando SetCoordinates para mudar o sistema ambiente, ou for\303\247ar a quest\303\243o, definindo o vetor

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLUknUlRBQkxFR0YoNiUiKlMtWm8lLUknTUFUUklYR0YoNiQ3JTcjKiZJInhHRigiIiJJInlHRihGOTcjLCZGOkY5SSJ6R0YoRjk3IywmRjhGOUY9ISIiNyVRInhGKFEieUYoUSJ6RigmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRkU2Iy9JJCVpZEdGKEYx

ent\303\243o escrevendo

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2J1EiRkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj4tSSNtb0dGJDYtUSM6PUYnL0Y9USdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlctRiM2Jy1GLDYlUSxWZWN0b3JGaWVsZEYnL0Y6RjgvRj1RJ2l0YWxpY0YnLUZCNj5RMCZBcHBseUZ1bmN0aW9uO0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy9GN0Y7RjkvJSp1bmRlcmxpbmVHRjsvJSpzdWJzY3JpcHRHRjsvJSxzdXBlcnNjcmlwdEdGOy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y7LyUrZXhlY3V0YWJsZUdGOy8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjsvJSpjb252ZXJ0ZWRHRjsvJStpbXNlbGVjdGVkR0Y7LyUscGxhY2Vob2xkZXJHRjsvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjtGRUZHRklGS0ZNRk9GUUZTL0ZWUSYwLjBlbUYnL0ZZRmNxLUkobWZlbmNlZEdGJDYkLUYjNigtRiw2J1EiVkYnRjZGOUY8Rj8tRkI2LVEiLEYnRkVGRy9GSkY4RktGTUZPRlFGU0ZicS9GWVEsMC4zMzMzMzMzZW1GJy1GLDYlUSpjYXJ0ZXNpYW5GJ0ZpbkZqbi1GZnE2Ji1GIzYpLUYsNiVRInhGJ0ZpbkZqbkZdci1GLDYlUSJ5RidGaW5Gam5GXXItRiw2JVEiekYnRmluRmpuRmRwRkVGRS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZkcEZFRkVGZHBGRUYrRmRwRkVGK0ZkcEZFRitGZHBGRQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJGR0YoLUknUlRBQkxFR0YoNiUiKmc0Wm8lLUknTUFUUklYR0YoNiU3JTcjKiZJInhHRigiIiJJInlHRihGOTcjLCZGOkY5SSJ6R0YoRjk3IywmRjhGOUY9ISIiNyVRInhGKFEieUYoUSJ6RihRJmZpZWxkRigmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRkY2Iy9JJCVpZEdGKEYx

O rotacional de F pode ser calculado pelo comando

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElQ3VybEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNidRIkZGJy8lJWJvbGRHRjEvRjBRJmZhbHNlRicvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRkIvJStleGVjdXRhYmxlR0ZAL0YzUSdub3JtYWxGJ0ZHRkVGRw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqKz1abyUtSSdNQVRSSVhHRig2JTclNyMhIiJGNDcjLCRJInhHRihGNTclUSJ4RihRInlGKFEiekYoUSZmaWVsZEYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY+NiMvSSQlaWRHRihGLw==

ou pela nota\303\247\303\243o

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqUz9abyUtSSdNQVRSSVhHRig2JTclNyMhIiJGNDcjLCRJInhHRihGNTclUSJ4RihRInlGKFEiekYoUSZmaWVsZEYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUY+NiMvSSQlaWRHRihGLw==

Em ambos os casos, os vetores de base com barra indicam que o rotacional \303\251 novamente um VectorField.

A diverg\303\252ncia de F pode ser calculada pelo comando

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVErRGl2ZXJnZW5jZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNidRIkZGJy8lJWJvbGRHRjEvRjBRJmZhbHNlRicvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRkIvJStleGVjdXRhYmxlR0ZAL0YzUSdub3JtYWxGJ0ZHRkVGRw==

SSJ5RzYi

ou pela nota\303\247\303\243o

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

SSJ5RzYi

O gradiente do campo escalar

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoLCYqJClJInhHRigiIiMiIiJGMyokKUkieUdGKEYyRjNGMzcjRi4=

pode ser calculado pelo comando

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqITN1JW8lLUknTUFUUklYR0YoNiU3JDcjLCQqJiIiIyIiIkkieEdGKEY4Rjg3IywkKiZGN0Y4SSJ5R0YoRjhGODckUSJ4RihRInlGKFEmZmllbGRGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GQjYjL0kkJWlkR0YoRi8=

Os vetores de base com barra indicam que esse resultado \303\251 um VectorField. Aqui, \303\251 essencial incluir o nome do sistema de coordenadas no comando Gradient desde que o sistema ambiente n\303\243o seja o \303\272nico que rege as vari\303\241veis em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGQUZBRkE=.

Uma observa\303\247\303\243o semelhante se aplica ao c\303\241lculo do Laplaciano, dada por

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

IiIl

Se o sistema de coordenadas ambiente \303\251 alterado para

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

JkkqY2FydGVzaWFuRzYiNiRJInhHRiRJInlHRiQ=

o gradiente e Laplaciano, respectivamente, poderiam ter sido calculados com os comandos

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpR3JhZGllbnRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJmRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqK1tabyUtSSdNQVRSSVhHRig2JTckNyMsJComIiIjIiIiSSJ4R0YoRjhGODcjLCQqJkY3RjhJInlHRihGOEY4NyRRInhGKFEieUYoUSZmaWVsZEYoJkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZCNiMvSSQlaWRHRihGLw==

IiIl

ou com a nota\303\247\303\243o

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEmJkRlbDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRictSSNtaUdGJDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGNEYv

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSIqJXlnMyMqLUknTUFUUklYR0YoNiU3JDcjLCQqJiIiIyIiIkkieEdGKEY4Rjg3IywkKiZGN0Y4SSJ5R0YoRjhGODckUSJ4RihRInlGKFEmZmllbGRGKCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GQjYjL0kkJWlkR0YoRi8=

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

IiIl

<Text-field style="Heading 2" layout="Heading 2">Velocidade e Acelera\303\247\303\243o em Coordenadas Polares</Text-field>

Determinando express\303\265es para os vetores velocidade e acelera\303\247\303\243o em coordenadas n\303\243o Cartesianas \303\251 uma tarefa t\303\255pica em mec\303\242nica. Para obter estas express\303\265es em coordenadas polares, relembrar

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyQtSSdSVEFCTEVHRig2JSIqb2ZFKCkpLUknTUFUUklYR0YoNiM3JDcjLUkkY29zR0YlNiNJJnRoZXRhR0YoNyMtSSRzaW5HRiVGNyZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRigtRi02JSIqQ10xOCotRjE2IzckNyMsJEY6ISIiRjRGPDckLUY8NiMvSSQlaWRHRihGLy1GPDYjL0ZNRkI=

como representa\303\247\303\265es dos vetores de base unit\303\241ria movendo (ou local) em coordenadas polares. Introduzir os s\303\255mbolos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiakYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=

no lugar dos vetores de base i e j, e escreva LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjItSSNtb0dGJDYtUSIuRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlVGMg==

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIiLCYqJi1JJGNvc0dGJTYjLUkmdGhldGFHRig2I0kidEdGKEYwSSJpR0YoRjBGMComLUkkc2luR0YlRjVGMEkiakdGKEYwRjA3I0Yx

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiYkdGKDYjIiIjLCYqJi1JJHNpbkdGJTYjLUkmdGhldGFHRig2I0kidEdGKCIiIkkiaUdGKEY6ISIiKiYtSSRjb3NHRiVGNUY6SSJqR0YoRjpGOjcjRjE=

Pr\303\263ximo, expressar i e j em termos dos vetores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUSJyRicvRjZGNC9GOVEnaXRhbGljRicvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUScmIzk1MjtGJ0Y1L0Y5USdub3JtYWxGJ0ZCLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGQg==, onde, para evitar conflitos de nomes, use os s\303\255mbolos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiRUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUSJyRicvRjZGNC9GOVEnaXRhbGljRicvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiRUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUScmIzk1MjtGJ0Y1L0Y5USdub3JtYWxGJ0ZCLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGQg==.

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJxR0YoPCQvSSJpR0YoKiYsJiomLUkkc2luR0YlNiMtSSZ0aGV0YUdGKDYjSSJ0R0YoIiIiJkkiRUdGKDYjRjhGOyEiIiomJkY9NiNJInJHRihGOy1JJGNvc0dGJUY2RjtGO0Y7LCYqJClGNCIiI0Y7RjsqJClGREZJRjtGO0Y/L0kiakdGKComRkZGPywmKiZGNEY7RkFGO0Y7KiZGPEY7RkRGO0Y7Rjs3I0Yu

Escreva o vetor posi\303\247\303\243o como

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj4tSSNtb0dGJDYtUSM6PUYnL0Y9USdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlctRiM2Jy1GLDYlUS9Qb3NpdGlvblZlY3RvckYnL0Y6RjgvRj1RJ2l0YWxpY0YnLUZCNj5RMCZBcHBseUZ1bmN0aW9uO0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy9GN0Y7RjkvJSp1bmRlcmxpbmVHRjsvJSpzdWJzY3JpcHRHRjsvJSxzdXBlcnNjcmlwdEdGOy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUnb3BhcXVlR0Y7LyUrZXhlY3V0YWJsZUdGOy8lKXJlYWRvbmx5R0Y7LyUpY29tcG9zZWRHRjsvJSpjb252ZXJ0ZWRHRjsvJStpbXNlbGVjdGVkR0Y7LyUscGxhY2Vob2xkZXJHRjsvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjtGRUZHRklGS0ZNRk9GUUZTL0ZWUSYwLjBlbUYnL0ZZRmNxLUkobWZlbmNlZEdGJDYkLUYjNiUtRmZxNiYtRiM2KUYrLUYjNilGKy1GIzYnLUYsNiVRInJGJ0ZpbkZqbkZcby1GZnE2JC1GIzYlLUYsNiVRInRGJ0ZpbkZqbkZkcEZFRkVGZHBGRS1GQjYtUTEmSW52aXNpYmxlVGltZXM7RidGRUZHRklGS0ZNRk9GUUZTRmJxRmRxLUYjNictRiw2JVEkY29zRidGOUZFRlxvLUZmcTYkLUYjNidGKy1GIzYnLUYsNiVRJyYjOTUyO0YnRjlGRUZcb0ZlckZkcEZFRitGZHBGRUZFRmRwRkVGK0ZkcEZFLUZCNi1RIixGJ0ZFRkcvRkpGOEZLRk1GT0ZRRlNGYnEvRllRLDAuMzMzMzMzM2VtRictRiM2KUYrRmByRlxzLUYjNictRiw2JVEkc2luRidGOUZFRlxvRmRzRmRwRkVGK0ZkcEZFRitGZHBGRUZFLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmRwRkVGRUZkcEZFRitGZHBGRUYrRmRwRkVGK0ZkcEZF

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLUknUlRBQkxFR0YoNiUiKisjKltvJS1JJ01BVFJJWEdGKDYjNyQ3IyomLUkickdGKDYjSSJ0R0YoIiIiLUkkY29zR0YlNiMtSSZ0aGV0YUdGKEY6Rjw3IyomRjhGPC1JJHNpbkdGJUY/RjwmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRkY2Iy9JJCVpZEdGKEYx

e diferencie com rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5 para obter

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNSdEdGKC1JJ1JUQUJMRUdGKDYlIipTN1xvJS1JJ01BVFJJWEdGKDYjNyQ3IywmKiYtSSVkaWZmR0YmNiQtSSJyR0YoNiNJInRHRihGPyIiIi1JJGNvc0dGJTYjLUkmdGhldGFHRihGPkZARkAqKEY8RkAtSSRzaW5HRiVGQ0ZALUY6NiRGREY/RkAhIiI3IywmKiZGOUZARkdGQEZAKihGPEZARkFGQEZJRkBGQCZJJ1ZlY3RvckdGJTYjSSdjb2x1bW5HRig3Iy1GUDYjL0kkJWlkR0YoRjE=

Substitua os vetores de base impl\303\255cita i e j com seus equivalentes em termos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUSJyRicvRjZGNC9GOVEnaXRhbGljRicvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JC1GLzYlUScmIzk1MjtGJ0Y1L0Y5USdub3JtYWxGJ0ZCLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGQg==, obtendo

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLUkidkdGKDYjSSJ0R0YoLCYqJi1JJWRpZmZHRiY2JC1JInJHRihGL0YwIiIiJkkiRUdGKDYjRjdGOEY4KihGNkY4LUY0NiQtSSZ0aGV0YUdGKEYvRjBGOCZGOjYjRkBGOEY4Ris=

Similarmente, para obter o vetor acelera\303\247\303\243o, diferencie o vetor posi\303\247\303\243o duas vezes, obtendo

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

ent\303\243o, substitua os vetores de base i e j para obter

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLCYtSSVkaWZmR0YmNiQtSSJyR0YoNiNJInRHRigtSSIkR0YmNiRGNSIiIyIiIiomRjJGOiktRjA2JC1JJnRoZXRhR0YoRjRGNUY5RjohIiJGOiZJIkVHRig2I0YzRjpGOiomLCYqKEY5RjotRjA2JEYyRjVGOkY9RjpGOiomRjJGOi1GMDYkRj9GNkY6RjpGOiZGQzYjRkBGOkY6NyMsJiomLCYtRjA2JEZIRjVGOkY7RkFGOkZCRjpGOiomLCZGR0Y6KiZGMkY6LUYwNiRGPUY1RjpGOkY6Rk1GOkY6

<Text-field style="Heading 1" layout="Heading 1">O Pacote Physics </Text-field>

<Text-field style="Heading 2" layout="Heading 2">Vetores Projetados</Text-field>

<Text-field style="Heading 3" layout="Heading 3">Inicializa\303\247\303\265es</Text-field>

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

Um vetor projetado \303\251 aquele para o qual os componentes s\303\243o indicados explicitamente. Por exemplo, o seguinte vetor V \303\251 um vetor projetado.

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLCgqJi1JImZHRig2JUkieEdGJkkieUdGJkkiekdGJiIiIkkjX2lHRiZGNkY2KiYtSSJnR0YoRjJGNkkjX2pHRiZGNkY2KiYtSSJoR0YoRjJGNkkjX2tHRiZGNkY2NyNGLg==

No modo de texto (matem\303\241tica 1D) vetores de base s\303\243o introduzidos com o s\303\255mbolo "_" na frente da letra. A convers\303\243o de um s\303\255mbolo para matem\303\241tica 2D torna o modo de entrada do vetor de base como um caractere com um s\303\255mbolo "^" sobreposto. Para introduzir s\303\255mbolo "_" durante a digita\303\247\303\243o em modo math, o caractere de escape (\134) deve ser digitado.

No presente momento, tr\303\252s sistemas de coordenadas s\303\243o reconhecidos: Cartesianas, cil\303\255ndricas e esf\303\251ricas.

Se o par\303\242metro mathematicalnotation \303\251 definido como true, ent\303\243o vetores de base unit\303\241rio s\303\243o exibidos como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRJyYjOTU1O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21vR0YkNi1RIl5GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGTkY1L0ZLUSV0cnVlRidGNQ==, onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy \303\251 o s\303\255mbolo apropriado da Tabela 2.

Coordenadas s\303\243o alteradas com o comando ChangeBasis, com sistemas referenciados pelo n\303\272mero conforme Tabela 2.

N\303\272mero de Refer\303\252ncia

Sistema

Vetores de Base

Vari\303\241veis de Coordenadas

Cartesiana

i, j, k

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEieUYnRi9GMkY1LUYsNiVRInpGJ0YvRjJGOQ==

Cil\303\255ndrica

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EnJiM5NjE7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYnUScmIzk2NjtGJ0YvRjJGNUY4RjotRiw2J1Eia0YnRi9GMkY1RjhGPg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NjY7RidGL0YyRjUtRiw2JVEiekYnL0YwRj0vRjNRJ2l0YWxpY0YnRjI=

Esf\303\251rica

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EickYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSIsRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2J1EnJiM5NTI7RidGL0YyRjVGOEY6LUYsNidRJyYjOTY2O0YnRi9GMkY1RjhGPg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NTI7RicvRjBGPUY5RjUtRiw2JVEnJiM5NjY7RidGU0Y5Rjk=

Tabela 2 Os sistemas de coordenadas suportado no pacote Physics

No sistema de coordenadas esf\303\251ricas, 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onde LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= \303\251 medido para baixo do eixo-LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= positivo; e 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy \303\251 medido a partir do eixo-LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== positivo sentido anti-hor\303\241rio em torno do eixo-LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

Em coordenadas cil\303\255ndricas, o vetor V \303\251 dado por

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWY0dGKCwoKiYsJiomLUkiZkdGKDYlSSJ4R0YmSSJ5R0YmSSJ6R0YmIiIiLUkkY29zR0YlNiNJJHBoaUdGJkY4RjgqJi1JImdHRihGNEY4LUkkc2luR0YlRjtGOEY4RjhJJV9yaG9HRiZGOEY4KiYsJiomRjJGOEZARjghIiIqJkY+RjhGOUY4RjhGOEklX3BoaUdGJkY4RjgqJi1JImhHRihGNEY4SSNfa0dGJkY4Rjg3I0Yu

e em coordenadas esf\303\251ricas, \303\251 dada por

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWc0dGKCwoKiYsKCooLUkiZkdGKDYlSSJ4R0YmSSJ5R0YmSSJ6R0YmIiIiLUkkc2luR0YlNiNJJnRoZXRhR0YmRjgtSSRjb3NHRiU2I0kkcGhpR0YmRjhGOCooLUkiZ0dGKEY0RjhGOUY4LUY6Rj9GOEY4KiYtSSJoR0YoRjRGOC1GPkY7RjhGOEY4SSNfckdGJkY4RjgqJiwoKihGMkY4RkhGOEY9RjhGOCooRkJGOEZIRjhGREY4RjgqJkZGRjhGOUY4ISIiRjhJJ190aGV0YUdGJkY4RjgqJiwmKiZGMkY4RkRGOEZPKiZGQkY4Rj1GOEY4RjhJJV9waGlHRiZGOEY4NyNGLg==

Em cada caso, note que n\303\243o as substitui\303\247\303\265es s\303\243o feitas nos coeficientes. Apenas os vetores de base s\303\243o alterados, deixando o usu\303\241rio a tarefa de implementar as substitui\303\247\303\265es apropriadas nos coeficientes.

Outra caracter\303\255stica dos vetores projetados \303\251 demonstrada por meio da adi\303\247\303\243o dos seguintes dois vetores dados em coordenadas esf\303\251ricas.

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWMUdGKCwoKiYmSSJhR0YoNiMiIiJGM0kjX3JHRiZGM0YzKiYmSSJiR0YoRjJGM0knX3RoZXRhR0YmRjNGMyomJkkiY0dGKEYyRjNJJV9waGlHRiZGM0YzNyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNWMkdGKCwoKiYmSSJhR0YoNiMiIiMiIiJJI19yR0YmRjRGNComJkkiYkdGKEYyRjRJJ190aGV0YUdGJkY0RjQqJiZJImNHRihGMkY0SSVfcGhpR0YmRjRGNDcjRi4=

A soma, ou seja,

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

LCgqJkkjX3JHJSpwcm90ZWN0ZWRHIiIiLCYmSSJhRzYiNiNGJkYmJkYpNiMiIiNGJkYmRiYqJkknX3RoZXRhR0YlRiYsJiZJImJHRipGK0YmJkYzRi1GJkYmRiYqJkklX3BoaUdGJUYmLCYmSSJjR0YqRitGJiZGOUYtRiZGJkYm

\303\251 calculado sem levar em conta o ponto de raiz dos vetores. O design assume que o espa\303\247o Cartesiano subjacente seja plano (curvatura zero), de modo que mesmo se os vetores forem dados em coordenadas n\303\243o Cartesianas, a transla\303\247\303\243o paralela \303\251 permitida, e os vetores podem ser adicionados. Este recurso exclui muitas das funcionalidades gr\303\241ficas fornecidas nos pacotes VectorCalculus.

Outra conseq\303\274\303\252ncia de ter os vetores de base apenas como s\303\255mbolos, e n\303\243o fun\303\247\303\265es de posi\303\247\303\243o torna-se aparente no c\303\241lculo dos vetores velocidade e acelera\303\247\303\243o em mec\303\242nica. Suponha que definimos a posi\303\247\303\243o de uma part\303\255cula em coordenadas polares (uma especializa\303\247\303\243o do sistema cil\303\255ndrico), por meio do vetor

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoKiYtSSRyaG9HRiY2I0kidEdGKCIiIkklX3Job0dGJkYzNyNGLg==

ent\303\243o diferencie com rela\303\247\303\243o a LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== para obter a velocidade. Definimos o err\303\264neo

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNidRIlJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y6LUYjNiUtSSNtb0dGJDYtUSIuRicvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVS8lK2V4ZWN1dGFibGVHRjdGQy9GUkY0RlhGQw==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMqJi1JJWRpZmZHRiY2JC1JJHJob0dGJjYjSSJ0R0YoRjMiIiJJJV9yaG9HRiZGNEYr

porque o vetor de base LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JC1JJm1vdmVyR0YkNiUtRiw2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUkjbW9HRiQ2LVEiXkYnRjovJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZTRjovRlBRJXRydWVGJ0Y6RisvRjhGVy9GO1EnaXRhbGljRic= \303\251 apenas um s\303\255mbolo, sem qualquer depend\303\252ncia expl\303\255cita sobre a posi\303\247\303\243o e assim, tempo.

Se tentarmos escrever a depend\303\252ncia posicional expl\303\255cita no vetor posi\303\247\303\243o, como em

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoKiYtSSRyaG9HRiY2I0kidEdGKCIiIi1JJV9yaG9HRiY2JEYvLUkkcGhpR0YmRjFGMzcjRi4=

diferencia\303\247\303\243o leva \303\240

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLUklZGlmZkdGJjYkLUkkcmhvR0YmNiNJInRHRihGNCIiIi1JJV9yaG9HRiY2JEYxLUkkcGhpR0YmRjNGNUY1KiZGMUY1LCYqJi0tJkkiREdGJTYjRjU2I0Y3RjhGNUYuRjVGNSomLS0mRkE2IyIiI0ZDRjhGNS1GLzYkRjlGNEY1RjVGNUY1Ris=

onde as derivadas do vetor de base movendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRJyYjOTYxO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21vR0YkNi1RIl5GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGTkY1L0ZLUSV0cnVlRidGNQ== ainda deve ser calculado. Dada a complexidade da nota\303\247\303\243o, vamos ir a este c\303\241lculo em uma forma mais parecida com o m\303\251todo utilizado no pacote VectorCalculus. No entanto, vamos encontrar esse c\303\241lculo ser mais simples de implementar no pacote Physics.

N\303\263s podemos facilmente obter express\303\265es para os vetores de base i e j em termos dos vetores de base movendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRJyYjOTYxO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21vR0YkNi1RIl5GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGTkY1L0ZLUSV0cnVlRidGNQ== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRJyYjOTY2O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21vR0YkNi1RIl5GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGTkY1L0ZLUSV0cnVlRidGNQ== como se segue.

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1JJW1zdWJHRiQ2JS1GLDYnUSJlRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPy1GLDYlUSJqRicvRjtGOS9GPlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RKSZBc3NpZ247RicvRj5RJ25vcm1hbEYnLyUmZmVuY2VHRjwvJSpzZXBhcmF0b3JHRjwvJSlzdHJldGNoeUdGPC8lKnN5bW1ldHJpY0dGPC8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y8LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGW28tSSZtZnJhY0dGJDYoLUYjNictRiw2JVEsQ2hhbmdlQmFzaXNGJ0ZFRkYtRkw2PlEwJkFwcGx5RnVuY3Rpb247RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnL0Y4RjxGOi8lKnVuZGVybGluZUdGPC8lKnN1YnNjcmlwdEdGPC8lLHN1cGVyc2NyaXB0R0Y8LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRjwvJStleGVjdXRhYmxlR0Y8LyUpcmVhZG9ubHlHRjwvJSljb21wb3NlZEdGPC8lKmNvbnZlcnRlZEdGPC8lK2ltc2VsZWN0ZWRHRjwvJSxwbGFjZWhvbGRlckdGPC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGPEZPRlFGU0ZVRldGWUZlbkZnbi9Gam5RJjAuMGVtRicvRl1vRl1yLUkobWZlbmNlZEdGJDYkLUYjNictSSZtb3ZlckdGJDYlRkItRkw2LVEoJndlZGdlO0YnRk9GUUZTRlVGV0ZZRmVuRmduL0ZqblEsMC4xNjY2NjY3ZW1GJy9GXW9GW3NGZ24tRkw2LVEiLEYnRk9GUS9GVEY5RlVGV0ZZRmVuRmduRlxyL0Zdb1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjJGJ0ZPRl5xRk9GT0ZecUZPLUkpbXBoYW50b21HRiQ2JC1GIzYoLUYsNiVRJiZwaGk7RidGOkZPLUZMNi1RKSZlcXVhbHM7RidGT0ZRRlNGVUZXRllGZW5GZ25GaW5GXG8tRiM2J0ZcdEZmby1GYHI2JC1GLDYlUSJ0RidGRUZGRk9GXnFGT0YrRl5xRk8vJSxjb25zdHJhaW50c0dRLGhlaWdodC1vbmx5RicvJS5saW5ldGhpY2tuZXNzR0ZKLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmB1LyUpYmV2ZWxsZWRHRjwtRkw2LVEpJnZlcmJhcjtGJ0ZPRlFGUy9GVkY5RldGWUZlbkZnbi9Gam5RLDAuMTExMTExMWVtRicvRl1vRmp1LUZfbzYoLUZoczYkRmFvRml0RmpzRlx1Rl51RmF1RmN1Rl5xRk9GK0ZecUZP

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiZUdGKDYjSSJpR0YoLCYqJi1JJGNvc0dGJTYjLUkkcGhpR0YmNiNJInRHRigiIiJJJV9yaG9HRiZGOkY6KiYtSSRzaW5HRiVGNUY6SSVfcGhpR0YmRjohIiI3I0Yx

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiZUdGKDYjSSJqR0YoLCYqJi1JJHNpbkdGJTYjLUkkcGhpR0YmNiNJInRHRigiIiJJJV9yaG9HRiZGOkY6KiYtSSRjb3NHRiVGNUY6SSVfcGhpR0YmRjpGOjcjRjE=

Ent\303\243o definimos 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 parametricamente atrav\303\251s de

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN4dEdGKComLUkickdGJjYjSSJ0R0YoIiIiLUkkY29zR0YlNiMtSSRwaGlHRiZGMUYzNyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN5dEdGKComLUkickdGJjYjSSJ0R0YoIiIiLUkkc2luR0YlNiMtSSRwaGlHRiZGMUYzNyNGLg==

O vetor posi\303\247\303\243o em coordenadas Cartesianas \303\251 ent\303\243o

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJSR0YoLCYqKC1JInJHRiY2I0kidEdGKCIiIi1JJGNvc0dGJTYjLUkkcGhpR0YmRjJGNEkjX2lHRiZGNEY0KihGMEY0LUkkc2luR0YlRjdGNEkjX2pHRiZGNEY0NyNGLg==

de modo que o vetor velocidade \303\251 facilmente obtido como

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJWR0YoLCYqJi1JJWRpZmZHRiY2JC1JInJHRiY2I0kidEdGKEY2IiIiSSVfcmhvR0YmRjdGNyooRjNGNy1GMTYkLUkkcGhpR0YmRjVGNkY3SSVfcGhpR0YmRjdGNzcjRi4=

O vetor acelera\303\247\303\243o tamb\303\251m \303\251 facilmente obtido como

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoLCoqJi1JJWRpZmZHRiY2JC1JInJHRiY2I0kidEdGKC1JIiRHRiY2JEY2IiIjIiIiSSVfcmhvR0YmRjtGOyoqRjpGOy1GMTYkRjNGNkY7LUYxNiQtSSRwaGlHRiZGNUY2RjtJJV9waGlHRiZGO0Y7KihGM0Y7KUZARjpGO0Y8RjshIiIqKEYzRjstRjE2JEZCRjdGO0ZERjtGOzcjLCoqJi1GMTYkRj5GNkY7RjxGO0Y7Rj1GO0ZFRkcqKEYzRjstRjE2JEZARjZGO0ZERjtGOw==

ou melhor ainda, como

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLCYtSSVkaWZmR0YmNiQtSSJyR0YmNiNJInRHRigtSSIkR0YmNiRGNSIiIyIiIiomRjJGOiktRjA2JC1JJHBoaUdGJkY0RjVGOUY6ISIiRjpJJV9yaG9HRiZGOkY6KiYsJiooRjlGOi1GMDYkRjJGNUY6Rj1GOkY6KiZGMkY6LUYwNiRGP0Y2RjpGOkY6SSVfcGhpR0YmRjpGOjcjLCYqJiwmLUYwNiRGRkY1RjpGO0ZBRjpGQkY6RjoqJiwmRkVGOiomRjJGOi1GMDYkRj1GNUY6RjpGOkZLRjpGOg==

Note que nenhuma disposi\303\247\303\243o especial teve que ser feito para garantir que as derivadas temporais foram expressas com a nota\303\247\303\243o ponto como em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbW92ZXJHRiQ2JS1GIzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZILUkjbWlHRiQ2JVEmJnBoaTtGJy8lJ2l0YWxpY0dGOUY0RjQtRjE2L1EpJnBlcmlvZDtGJy8lJWJvbGRHUSV0cnVlRicvRjVRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlhGN0Y6RjxGPkZARkJGREZGRkkvRkVGVi1JKG1mZW5jZWRHRiQ2JC1GTDYlUSJ0RicvRlBGVi9GNVEnaXRhbGljRidGNEY0 . Esta \303\251 uma outra caracter\303\255stica \303\272til do pacote Physics.

<Text-field style="Heading 2" layout="Heading 2">Vetores N\303\243o Projetados</Text-field>

<Text-field style="Heading 3" layout="Heading 3">Inicializa\303\247\303\265es</Text-field>

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH

<Text-field style="Heading 3" layout="Heading 3">Introdu\303\247\303\243o</Text-field>

Vetores projetados exigem indica\303\247\303\265es expl\303\255citas de componentes. Nos vetores n\303\243o projetados, entrar com um "_" colocado posterior ao s\303\255mbolo, pode ser manipulado como componentes sans s\303\255mbolos. Esta provavelmente \303\251 a propriedade mais significativa dos vetores no pacote Physics.

Vamos ilustrar esse recurso atrav\303\251s de v\303\241rios exemplos.

JSFH

<Text-field style="Heading 3" layout="Heading 3">Exemplo 1</Text-field>

Obter a equa\303\247\303\243o vetorial de um plano que passa por tr\303\252s pontos dados. Em seguida, especifique a f\303\263rmula do plano atrav\303\251s dos tr\303\252s pontos 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

Seja os pontos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY1LUYsNiVRImNGJ0YvRjJGOQ==, e deixe os vetores posi\303\247\303\243o Cartesianos para que estes pontos sejam LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiYUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSIsRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2J1EiYkYnRi9GMkY1RjhGOi1GLDYnUSJjRidGL0YyRjVGOEY+. Definir os vetores 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, e 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 por

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNBX0dGKCwmSSNjX0dGKCIiIkkjYV9HRighIiI3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNCX0dGKCwmSSNiX0dGKCIiIkkjYV9HRighIiI3I0Yu

Com o par\303\242metro mathematicalnotation definido true, vetores n\303\243o-projetados s\303\243o exibidos com uma seta transposta. No modo texto (matem\303\241tica 1D) eles s\303\243o inseridos com um s\303\255mbolo "_". No modo de entrada 2D , o "_" deve ser precedido pelo caractere de escape (\134). O s\303\255mblo ser\303\241 vis\303\255vel como entrada, mas vai desaparecer sobre a sa\303\255da. Se a matem\303\241tica 1D \303\251 convertida para a matem\303\241tica 2D (como fizemos aqui), ent\303\243o a entrada ser\303\241 exibida a nota\303\247\303\243o com a seta.

Os vetores A e B est\303\243o no plano desejado. Se r \303\251 o vetor de posi\303\247\303\243o de um ponto arbitr\303\241rio no plano, ent\303\243o o vetor 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 dado pelo

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNDX0dGKCwmSSNyX0dGKCIiIkkjYV9HRighIiI3I0Yu

tamb\303\251m se situa no plano. O valor absoluto do produto escalar triplo (ou misto) 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 \303\251 o volume do paralelep\303\255pedo definido pelos vetores A, B e C. Se estes vetores se situam em um plano comum, este volume deve ser zero. Portanto, a equa\303\247\303\243o do plano deve ser dada pelo

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkmbW92ZXJHRiQ2JS1GLDYlUSJDRidGL0YyLUYjNiUtRjY2LVEoJnNyYXJyO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZlbkYvRjIvRklGMS1GNjYtUSkmbWlkZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4xNjY2NjY3ZW1GJy9GTkZcby1JKG1mZW5jZWRHRiQ2JC1GIzYnLUZQNiUtRiw2JVEiQUYnRi9GMkZVRmduLUY2Ni1RKCZ0aW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXHAtRlA2JS1GLDYlUSJCRidGL0YyRlVGZ24vJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRIjBGJ0Y5RmNwRjk=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJxR0YoLy1JIi5HNiZGJi9JK21vZHVsZW5hbWVHRihJKFZlY3RvcnNHNiRGJi9GM0koUGh5c2ljc0dGJS9JKHBhY2thZ2VHRiZGNC9JMWhpZGVtb2R1bGVwcmVmaXhHRihJJXRydWVHRiY2JCwmSSNyX0dGKCIiIkkjYV9HRighIiItSSMmeEc2JUYmRjhGOjYkLCZJI2NfR0YoRkBGQUZCLCZJI2JfR0YoRkBGQUZCIiIhNyNGLg==

Para calcular esta f\303\263rmula com os pontos dados, utilize

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNxcUdGKC8sKiomIiM7IiIiSSJ4R0YmRjIhIiIiI0tGMiomRjVGMkkieUdGJkYyRjIqJiIjU0YySSJ6R0YmRjJGMiIiITcjRi4=

que, com uma ligeira modifica\303\247\303\243o, simplifica para

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

LywqKiYiIiMiIiJJInhHJSpwcm90ZWN0ZWRHRiYhIiIqJiIiJUYmSSJ5R0YoRiZGJiomIiImRiZJInpHRihGJkYmRitGJiIiIQ==

JSFH

<Text-field style="Heading 3" layout="Heading 3">Exemplo 2</Text-field>

Para verificar a identidade vetorial

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

implemente os c\303\241lculos nos lados esquerdo e m\303\243o direito separadamente, como em

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqUklHSFRTSURFRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSdleHBhbmRGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2Ly1GNjYuUSgmbmFibGE7RidGOS9JK21zZW1hbnRpY3NHRiRRKFBoeXNpY3NGJ0Y7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjExMTExMTFlbUYnLUYsNiVRImZGJ0YvRjItRlM2JC1GIzYpLUYsNiVRInhGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZnbi9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRmVvLUYsNiVRInpGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYuUSkmbWlkZG90O0YnRjlGWkY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjE2NjY2NjdlbUYnL0ZORmdwLUkmbW92ZXJHRiQ2JS1GLDYlUSJWRidGL0YyLUY2Ni1RJyZyYXJyO0YnRjlGO0Y+L0ZBRjFGQkZERkZGSEZKRk1GSEZeby1GNjYuUScmcGx1cztGJ0Y5RlpGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZncUZbb0Zeby1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRmduL0ZORmhuLUZTNiQtRiM2KEZXRmNwRmlwRl5vRmFwRjlGOUZhcEY5RjlGYXBGOQ==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlMRUZUU0lERUdGKCwqKiYtSSJmR0YoNiVJInhHRiZJInlHRiZJInpHRiYiIiItSStEaXZlcmdlbmNlRzYlRiYvSShwYWNrYWdlR0YmSShWZWN0b3JzRzYkRiYvSSttb2R1bGVuYW1lR0YoSShQaHlzaWNzR0YlL0kxaGlkZW1vZHVsZXByZWZpeEdGKEkldHJ1ZUdGJjYjLUkjVl9HRihGMkY2RjYtSSIuRzYmRiYvRj9GPEY6RkE2JComLUklZGlmZkdGJjYkRjBGM0Y2SSNfaUdGJkY2RkVGNi1GSDYkKiYtRk42JEYwRjRGNkkjX2pHRiZGNkZFRjYtRkg2JComLUZONiRGMEY1RjZJI19rR0YmRjZGRUY2NyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpSSUdIVFNJREVHRigsKiomLUkiZkdGKDYlSSJ4R0YmSSJ5R0YmSSJ6R0YmIiIiLUkrRGl2ZXJnZW5jZUc2JUYmL0kocGFja2FnZUdGJkkoVmVjdG9yc0c2JEYmL0krbW9kdWxlbmFtZUdGKEkoUGh5c2ljc0dGJS9JMWhpZGVtb2R1bGVwcmVmaXhHRihJJXRydWVHRiY2Iy1JI1ZfR0YoRjJGNkY2LUkiLkc2JkYmL0Y/RjxGOkZBNiQqJi1JJWRpZmZHRiY2JEYwRjNGNkkjX2lHRiZGNkZFRjYtRkg2JComLUZONiRGMEY0RjZJI19qR0YmRjZGRUY2LUZINiQqJi1GTjYkRjBGNUY2SSNfa0dGJkY2RkVGNjcjRi4=

ent\303\243o, compare as express\303\265es resultantes com

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEpTEVGVFNJREVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSgmbWludXM7RicvRjNRJ25vcm1hbEYnL0krbXNlbWFudGljc0dGJFEoUGh5c2ljc0YnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk8tRiw2JVEqUklHSFRTSURFRidGL0YyLyUrZXhlY3V0YWJsZUdGQEY5

IiIh

Alternativamente, utilizando os formul\303\241rios inertes para o operador diverg\303\252ncia, podemos escrever

expand(%Divergence(f*V_));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomSSJmR0YoIiIiLUksJURpdmVyZ2VuY2VHRig2I0kjVl9HRihGL0YvLUkiLkc2JkYmL0krbW9kdWxlbmFtZUdGKEkoVmVjdG9yc0c2JEYmL0Y4SShQaHlzaWNzR0YlL0kocGFja2FnZUdGJkY5L0kxaGlkZW1vZHVsZXByZWZpeEdGKEkldHJ1ZUdGJjYkLUkqJUdyYWRpZW50R0YoNiNGLkYzRi9GKw==

Para verificar a identidade vetorial

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

implemente os c\303\241lculos nos lados esquerdo e m\303\243o direito separadamente, como em

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

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlMRUZUU0lERUdGKC1JJUN1cmxHNiVGJi9JKHBhY2thZ2VHRiZJKFZlY3RvcnNHNiRGJi9JK21vZHVsZW5hbWVHRihJKFBoeXNpY3NHRiUvSTFoaWRlbW9kdWxlcHJlZml4R0YoSSV0cnVlR0YmNiMtRi82Iy1JI1ZfR0YoNiVJInhHRiZJInlHRiZJInpHRiY3I0Yu

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

ent\303\243o, compare as express\303\265es resultantes com

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

IiIh

Usando as formas inertes do operador rotacional, podemos alternativamente escrever

expand(%Curl(%Curl(V_)));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJi1JKiVHcmFkaWVudEdGKDYjLUksJURpdmVyZ2VuY2VHRig2I0kjVl9HRigiIiItSSslTGFwbGFjaWFuR0YoRjIhIiJGKw==

JSFH

yIpyIr<K_Tn^T^;N:L`^C:yIu@K\\PqkhpvF:CZ:N;xYqo[;_fiOf_CS;P:FZyYUCND<KB`KC`kMXkEXLSTlITLStLMTLMTLQtmTPmTP]x^b;Gb;GBLN\\LN\\::::FZOF]S>^V>^`>]Rn^pn^Zn^p^bpV_en`>_b>OboNb>_b>_B:::::ry;pB\\ZKa:AR:?K;@k:HjB@jyMfOL;Hj:@J:B::FZ<^Z?VZ@FZ;FZ;J:B::F:AB;[j:LZ>VZ?nZ=nZ@NZ<V:@J:@K;HjJ@MCLjZ@o<@prDlCLk:AsJAuZEmbENc<yjEPsHlD@Y;EsSLM=HNLDTSEv;QmB@J:DJ;Dj:LJ;Dj;V:<J:FZKNZLF^=F`;Gd\\N`[Gh;PbKPdMFnk`ZyQUSr:=J;@k;@K:x]pIgd?[PPcgplcGba?d@?nm`yniq=WoBGtNI\\b`_iAdY@oDg_[@o]>dSoyuwnainPvqbX^JKwlMtETgeK;Qm<xsmITdil^pp@HNGQm<xSoAKoEk?]Po\\JdUky\\t]\\T_p<aeK=WmIexCFicibdm=MMolKeYQNYNNo`bOwVFtbXhSoq[p]_@_SinfXh@GpGqftajHhvon`cWwVFtfXhSoq_x_LOmU``oqkbots^oIQdIPdT<jYEoAkTPMA]@^dI`dTpnGic]Omonkew_Oi^dYlMofhHpGQ]Ai`QPwLhxCGomxdRovGXfTXsoA_oIcd`wNqtsVnRovlhyDgaDOgf_tP=NdwNdd_gN=bLAEVMTjecGM]MatPffU@oLq]aW\\NpbeOawirpXsPWpIFvCPeAI[Pxfrvj^`tK>oiV_aaeyNxEouLgxqw[vijeoylvmnyjd`tK>OUSy?XvmiyObFOyp=F[CE=WFJYV\\SyMkIsyGwIvdgXHA_jpxWYbFAk>Nw]V`LxwdylwNeSYofXh@kldYLqUcd`OqtsVNDuXIoKQWuhtNIue:OxHcg]UYGUSeSwVG\\^OynPi^`tppprXx@?qmIe=vhDXfqOkdopPytX>gPmIUoAUOGUSeUwVHDNdwJEQWea=fYucLov`e;rect]ttLQuttRnXWIhpMPwLexcEOgeykqVGHx`MPwLUwLUdUUY]usU>tkPyMedCgXHjxDoXBUghom;pUcb`qnttbP=NmUh@:beGWmutRoVGV_OY^Oq^`hsW;ZcFom<VSKTwMTdHOfTx@cleYLoIccXpMGeaeKfFdQL;:LSdaG:cfXC?:LtXs`e;:dC:JDmpdUGNP_L_@oSYOf:\\ntobGiEP=v^dQlQpf`HpGQ=eS_Oy^eYDGTmU<v?ASoEs@eSGW>xUcB_SEog@fYDobHuc\\_Gl_G_t_nNudS?P`N<M_@;C?qtOkdsbl`n@iVMQtTQQ<PWGtTdut[PLMLk_PlI]uOTnfllpEV[`THMkZlvMUPv<qZ`v=QUcDr>\\M<XnIMLf=U\\XMl=Rf@tHIM;EM\\TTnIJ?QKTYl[LsfmJOEkfTTfUt:EKBaLSQrCQK\\evfPjb`kg]kI@k;pu]Lwe=SBYYPiqPYM^tV_XY_`wGTXp^gxWg^XvKv\\fnbMW`JwqTIl_vhpHn?^rZIqppcL_hSQ^Bh]aVbp>_GIZDxchic`nvbpcrWnKObl^bHFsL>dBiaBHjDycGa[Fht;FlBo]bWZDOZ@vcnFaB>c?>b^qvX`nYPjU^\\N_m^`fA`h_OmcFq=_lNXv^Pfk?dDg\\DQgpng]xd<xoN>yXHZN_uiy^y^Z;_jrFvChd?AtB@fRo_RHvxGeVhqPh`kN`_^vmO_@fr:iuMFlDn^?Qu[vjMg`Fisl_lQY]hVt:prA?^o@ceifTAhR>s^yahO[oNbQg]ZVqwQtaYyNHgb@uZYf\\^iLOyqg_T@_GHb<Xxpifmwo]pokFdagcx_dRG_tP\\JX[GvZ_n[M`nOn[L_aL^tm?cZHv<H_Ch^b`lVNZKO[cHmZ>s_Hm;_r\\@mK@b_^_<@aZf`cNg?ab`_mm?boQf_@obH_bnj^OsH_dD?ab>slFdNadDPjdh`NNa?o^OwcLg`NVp<GnCp]B^tLWb\\h^b@xIGdJowF?_CPwGOsI`ZSAboY^Q_`LpfKg[KIo?O[@`^RHl\\AnR`bBWc<PiDXjc`fZHlbNhL`g\\xjb^hm>nZ?\\;V`^nqcOnMnl?Q]Lxsw`@Csb]TlmrbCs:cV@cbR]d_KTZ_hFMTascf[D<_cJWR@;CASVnKWvMt^[EbsRbMxJ=CoGBc?BNsHn=fLkHj?IJwUTmEvEC[?vsmwcSh[mB]gfRQi]]C_CSs]SEiGsaV_YxR;eiGrCYy]ChECW?WHXofUms\\AsB=h=KXlmJIDTb`XltRlQU;LNJEkSDnFho;LsWLLAMy@dVghSLtk^XMT<olqMxLsidSj@JieRbewDitidWSUQQQuOiYePLVenfllwEVbUS_PrvmLTEt[Ls_XL?LnSLtK`r\\xKnlKvITNTyDTlvdmphRH@SCup:ljlMW>mN=Tnb@JJTT;lnPAtJLsFQjgLnfPLK<RCLvfLptpJ]auv@qwIpIeqYmuY]vPYVh=q?`juhxAmxlmSwQLhPLlLrK`rLDrtMycpkPENV=YFtslLPtplOISV=SZ]qkxw\\iPqXlZYpSilHeooer@QsPuSKauDDlBmjVeTN@j^DSN\\RHEOOLNS<NOLr^mK_TSnTpZDkFTLc@j=DSKYlRmJLmVK]WO]rSItLLL:QoBLPILVlURkQO\\ho>avFLxLas_hR<<OfAXGIKpaJx@SZTNLLtRPVS`odlMCAL[gcVQpDHowFnKPr?wbKIePPnO_wQ@cK`dGWpBa_Ia]o`]jivwqqgXZVGZQh`LouWxbBFlVIdZvf]ff>HkaO^rIZCAhdx`hwvwY^[n[H^d=QqrIolNwhhgHqsY@eDQdXftPgd=qgCVhcv]tWtlPqdwlQH_DWurnrRvpy?ZVX_^hyoAmpqvqhaoQrA_dd`hcAbrWniF]HiZfob<Gr@xZBhdqVeW^p\\f^]vmTYfYHrjWuWw^LavJPemF^YHpsOxEA_Wxoiwhror`N_cPnNGe[fa[_tlp[uXvkF`jWvk^e\\ViL>a>^rk_wBWvTPt;xs<dH]V=?FM=XxOGc]UDCyH[h;KCH?i\\AD=_T:cHckCBCEtACE[iMst^Ar?]DH?GnmBB;U<Sd]sR^[V:OR:KdscFVIh^]E@Kg^IEGWXLGsKER@uC;CIb?eKOUoaV?atBKFE;Y[]fguhmmX>_SseH\\ovp]XaAWUucOmH=mF<SU?UE?mVLcftGVh]SJMXAQYi_icMF@UXjur\\CVSMRZKs?MVlgdR?EXMnsDO?LQeULfHtsPPThn_Is>YqJHmBPXDDvKHKXPsJYUcuk_`LO`vDHmt@MZexu]laHqU]RsLpG@UgxSmXm]qyJEKCEujlOoXkE<Wv<rVaqwuQsxiDgbIAkSWsRVxjvvShrEvnWxpay_nAoUpxZYaY`xeXdga_gykuQb[^he^lffjfHfLPwRI_gBcshnkBRkVkCE<CUS?v\\wCDmBx;c=KulCrS_VCIFY[Vl;I>?B\\[ra_M?QncupnLX==o\\lJLaxS<t]LkSTPI]Nqdp<dsfTlrpNDENFHTLlqCAMbTlLpkfATrqNVET=aoGeUXaUVWcGWhxHl^_[rovP>xDanR@q`WdfGoR`mmW[lobp>bUw[pXcIiohvlrHgTf^NpqYqvwYwipfqv\\fqsMfsfNpNvv@^_MP`mQq\\@snGuFNn\\@u\\om_?`WvZZAoFGsF^d:@hP`gKFdC_mcHZ@@_PpcO^dl_b;Gsj>]\\GjDP_xYukPgQqxfhobhfgxeTIpevZfflEnrD^yl`dh`Zb`td>\\SNk:w`BHoFGaF_vCoxb>oH`e<VljNhYPg\\>`@WcDwfL@f]N`baj<_cdafZNn\\^s:`\\B@cHP[\\`_<`\\ShdYie^atB_srQbkx\\nVl=y]wwiWHgioprfZXG`mN^k^sPH[gn_ExbU@qPQh:htgAvwXlkyrnYxAOsywg;gc=ggNWgY^lvgdeW[OPgcAfdpfvphnysl`_PPg?_[PPsfVl`ns<h]NGbJ`dBaf:hDCE\\_DDGUJ_j@Pv^Ds`MO\\LrS`lSLLaQoBLpAQLK<KheNNUX`mKJqRf`LFduFHUgLNs\\Kl<SmtQ?XnM@NHxnVQKI\\MLYnTTL^mS_HNYDWOmrRaMNIuuatBHVk=R<HNyQV:DNYdnMlsXeRZTP_Pm=<klYnwlmk<O_IlbxXjeUelm`PVeHUwYs^\\y^qu_yvhQMApwbpvOiw;lpkYuAMpMMY?tWkuO\\TNgISLYUAIN:MxWdNAQV<mThiNJ`nuuLQhN_aqEMsEmmMmok\\ksuLFIySLsyo[L_mpFxZ?]j?k]YymOcsxuy>\\=`r`?aahp^xum^gwim;`g>Q[e`lshZbXwBXkCY^c^m]@]_oQIR:KVQOu]wVCARxwuTCfMkf:qUowW`?bDev[ac\\IyowrSmhnmikuSo=GEyrqwh?eV>SvrKwxgBQYD[wVpQGogvpmGsidUwfYys_WruSFUGyWeYsAgrcrM[DdwuJSYB?UTgsLKdO=EfqVfwTh_hCOgQStYQI_Uu>UbHWidyI:gimyCcGYeeD<[VL=i^aiw?DW]BEEg>gwTcwMYue[gckDoEHXgVfUY`GhSwEpmwy;RVOwIifrcrMXtSDk=lMeMMJlPI=SPuxjqoA@ju=pTutCLskmnq`WFTvuXxbytdtqr<YkejRMqJXu?qVr`XUqJMivaUsLluKPuk\\shxuFEulhvriLDYNHEUwIVUaoa]kkUynpsxIn@xMBHTetxOqtD\\rBQVcpKMlQ[qxTaXsetbEL]lKCYPGDXMlvkDUyao\\xLquPQarn@mutJq]uHPyiHTkQKAdtydthARehtnhMFV_m?]]qdaqkWGqVYvvf`HPy=`j;xkigZXA`volOWy=_cCGa[GxTgeFVwIXkbFoV`b>gfIXoWGi_Y`PHasijKypJnks`fdxcw_dIOuyesQrHOWwmbuSWFMfTAiwIhtOwnagfSxPErDsbYwYMawmsFHEXgugqahSuhbyUdSCG_y<iSc;hLsHOiyH=sgYwOsb:YFM=F_QfVodlAG<Yw>SSWshwWdq?e@ieuMidoDJ_BA=HQuWYysb?qodMT`Rr<VNtjAyLdUKk<QuUSmimYdWEtRwIBtpj`OLAMLLp_YmrHwmXu=aSHaMuutXUL[Epj`vo\\L?mrRAyNtrvtOfXPmqmdXYsUlvOwUVcnVc;?sryjOybmwawQluOdxpZc@a[QvDHwv^yy^]rVvkqoYYcchgK_rpa_Hhn\\vgIq^TWqcFk:As^ObBiurypafqmwr@QdeIuHAeqNygGhhxol^s>VbOhKOioWISCDI[Sr[BgoS[ogG?WfmI\\QrFQeHQyx?Y<iUm]ckeepwcqMfa]UHQE_sYRoTGuDE]EM]XT=h\\iXAGTbGVZwYcQbHeFXkuFsCCeFpydNUV^oGNHs=YjZinpHUSmw^@LnLv>MPPMW[uLD`RFeTEEy]ekFuTiTQsIpK<Ka`J?tTBEx>]qPUyP]Rj=JjYUHuvdEkmYWAeMhEVQEvNYouiLhaONXVAPvJXl^Iqt<MTTX;YX<LukuR^XJ;ArSUpBYv:DSwhNk@r;]rKEm[lJl\\s]ML<InEpNs=X@mV@qkC=nAMmW<PJmpfAd[OkwSEabCADbCRn]TFsRNov^aUNOS;;vJos^]UD_btCBmGFWcigMU?[rFEc`afGKum<T`\\vmLvJisXUmL<Nu@LVUTZDX=MqpPsXyt\\tRSTSO<ULXkFPrPuuQQoaLVkDuext>\\urdVOtOAUk@pvRLum`yWYWUPOWpm`amclLMmkuPRw\\vRtOxDTMqSKupPpV@Nd_ojBPZ@`gNAk^IlDNo>Fanw`HNcgWj?F\\XFe\\Nns^kJau<>i:FrGFkvGtKwfhycsP^of\\bnjvi\\OgubPejHs_gwkY_LG]fNsVPpOg_PosDgo[`tR_dRhrBwJ?sReBDIVkED_ysDMsF=CiOCQ]RCgBUar:EbCMt`oH]?wmoFYcD^KhBABbMG;mVn]rDYrdqdd=HPOxB?iO]YRMfQWttsSpOxSMVCgetQv`giVSia[bQiVbaXs[HUmCmsi;QRmYsSEdYUTFIVtKv<IGU]iQSYWIhGEYV_Uh;vc;sseb>sge_GZsB>]eNGE<YX?mTKmFBqR?SCn?dbUb\\YRCsc^]RWCt@OV@ch]MsfOc]EeG?iawFTkcb;gm?fhCe>EeN[fSUhCeeFAf[Orbmvj;r^OUWucDmSe?CCgW<aSRCXdaw;MT\\;uHeX>Si<?cEYRmSDguEd]Sr[YO[tWxST\\rrama=RcpqMLuL=k]mjdEov=TYHNShSmXJU]N>qJ=Gh?OaE`]O^ihxaHaop_vxVg@@vnfxx?nxAtvhykIxqpgc`vpfkvXvHickidhq]Cv`PvkwPeYpkLngZ^cuw\\JVbQn[HV_HXdlqrwg]]_r<qtTiqkF\\DVesIw:@oa__OIdPqpopjf@cSql<x\\wNdSxta_uPWymNv[PakyoNxy:>[T_[@@kxYfa@unhoJXuNW_\\qsxomoim`Oyw`o>@bOYgrf]cyd`AeoWuqa]USy[GQYIQQUqaH@SwgyvM[R]wf<qh]wdncwC;ypyU__dvUdg@X;qUdmMD@KfYkMITG\\Svxity^]a_W?m`vsd_xNnd^odXVtno`yAZax`?Ig=ooQAdpgthBRirbScFmw_srH]E]?U?oGqEtV[brWXYQWcwU=yVxgTQiWPqwgsTf_sDYtWCeDAglyU>AR;WevIxAYEEeTRgvQUYryVfYrRUwDgiZ?YA]Tt=gsQITGBQ_wxQtnIfocrW_Xnid^_C;SSbCubSfJcht[TCSw]SRCsXdUugwdMSB<EYCyX@ufIwbQsdbASHyI:EwoAw_yfI=tPMyViV`?CXEvnqI]yCMuslgwliEQAYHKH<iWCSvgYw_GFvyqHmvjYQ`tYLuOsMUu@QntjdISV]SUExk\\rLpppIV>PRIyvYHvQyY:xMeyQqpOfPUjTQQik?lUO]jxuNCdxg]ra@VCLXChXIUwYEm>YNQHlXePvlrPdVKDQIevdTtYEM]uxgPy[]nBhJ=TK_aSo]K^HQg<ooYj@doxdvmMR`qxAaRWhyklktdVko_kp^:h]_hhbih@A`mnlDwkPwuQWq]NsF>ZqaleQqjWuvNhY>hfQ___][_kjIfvvvX`aPXydX]^hbkOZw>qO@cUGf[AxMOnbitaFfZ>iO^io?aIVs?FqFPvew[H>iIae?yvuW_Wia;Ao@WrZqk=ojevqA?]Box]HoiGwVydRfdRpr?o_Y`hc^nDifVHoO`s]W\\`ytTFkHYf?A_FOwrpmOYnsXoOOb=?a]_w\\YpdGxTwp:WrO^m`Xpyxfh_qpWwPiiOOqcN\\VHoK@fTQnmxfgVe<XiNowCPn`?^qp__qrv`gUOs\\F`EA_xqsr^cHAi]yloAgoY[o>isG`qijYpdTyhAN[xQym@^fnkZG`OopUIsgws>pjsFk_fgFpbm^si>]aW`V`eCwihGpYVufxZJvoyohyVrhYcuIOChPSCXEfm[elssypXcIM[UPKamximbAO<=JCIuKTTKiQ?XxI\\KtXuEEVOmr^@YB\\oNlrspJuxN]]odpJeplIMujxxfhkZdThUKa=SR\\mDmTYEWFAQ<EjTDpC<qRdJMLnUQLRHjkXRkpRK@jJLWYUWkIOAdW[tN:lKdHNBAQh]R^UpX\\XFulvuR^vZIHrIobwG\\BXvHP_:W`VPs^nwN^jROvFXnFHpF?`?Q`Voh`b;OeBSSL_D:CrvMhGARGgFbkF_qI^yfXUfBWH]cf^=SJsRn_V^GdaOE<]SD;I?KvC;r^<t`LVLyN:LT\\MsfAn@`LAAN^DX:AThDtaerqDRp\\SHPOo@kRLW>XX;=VHMQ^LVrmlXIKPpOxMMhhQfttxIo`AMHAQqPKfdPFmss`rt`XqiPKlLAEOApmOivQPNcmxsUQW]QZ]SyeJuYVEPqaMM\\TMndL]PlbmWViMKHJLHnN=J;=t>mKchjJqJGAr]uJ?ltB<VjEt:\\m<Iw_lKdhOhMKo@KZEP>QV_USHUJLmjdXKU\\YEhJa`KPpWRmPeMSSDOdtV_PuJaoVtlCxJ;iR?DYApK:Tkt<\\=VqbhnVImH>mGG\\MNjS>cAhrSbBsHN_SMaVS]b?MD_mXC]tNuuIWS\\QXfuwtQxeAdoEgc;vIcdZaylexnyr@muxsshUuDaiUCVHKxEAUT;EiywKGVesxHsByircHPWaQ=eYxenWAq^LsgUj^XS=<SV<tNEmF@KD`S^LRUdJ>EMl<Qc@JKPkB@J@dxl<LRLOLiO;=NS\\S>INWdt;=lDUM^NoLg[?q^MG^kAc@HrKfsCXbpN_fOwa^]PImmOt_Q\\PPl;ahPH[RFjC`dmG`?Qs@Oc^OwkaZU@bgad?GmDAk?>rBI_K`o<HknVbFflcWZI@fsanRIa:QhLG\\pw^N^]k^sdHnUX\\Yh^HAwUV^@XfJNqBpqcnm?ImB@mcPgr>d>@sIv]a?v[H]<NykWZA@]pI\\oiei@oQYvB@r`i\\UO_GpybVlSvkFY`pyoNVvixrivou`qGWxI`l_`g@_auGpDoZcim<wZIo_evjWxqaTBKesauNwYrcHcoBF]rwQS>IFuswiQdPcExIIrsRsofeUu?uSVwr>=vC_VrMyekgtsXPSI@eFoWHFwROASqeIPQg`ExnKekmcvGvqYUOir=CSAsDQww<atdMTdgIZAWfoXXwUDuUkidtqtXISI;d^YRsCYiuWOYVp?YuMfmQS?ubechu_cOIXLGyOwU`CtduuLIthEcSWePKF\\KvNAWROr\\]iKYISYcUsUosxh[hmctTOh]YxRCiReDmcHlsE>SHbEIHMV=EsSmxnACE=dPoUQIb^USFyUg_BVQSeqt=Uck;UegCR[v\\?Go_skUTTOePeSjAfVaDHGGmmb<GgUIYRIILKHROimyXUCyKOTgPV;tlc`vbtKDxTfUnaUk\\POyMwvpTCmkJAsF]RkxY:dPXPWoUQ[=KbQOUInJ<k^IUMEJhlkExmpQpsio@PVMPotxRmxMuIu`YQ=AVJ=prdoLdJGYvSEMIusoTsLqQRIo`mZLqleAghv[>q_N^xwQ\\Lf^d?[sXbH>aOPd[`s=AefadhHwkIlrgl]Hk:Wk`Gkj>sxqtsGoAgnRxl_Vgy^_JV^IiZS>om?k\\N^enkeagh>]`i\\\\HibFw_Nd[wmq@uT`vhqoBFhrfZMIZPH_cWv_FfVfujxkOf_\\V^?ImIWqXam\\weOFe]^_Aa^@?]snxa>\\@FecX`]irNH\\A>^L>tC_amhhwN^f^m;`_]X`Bvl;>q`pZZHwJHZ`adA@kp?_GQ^:a[JVZ\\ad=@hFgZDfbrq^<nlPXbtVsNGe^NsfOZ>O^]@jCU?gsJoClOFG]iDkDVMTaCbLcsvadS=d=;wZ[I<EeGCU`cX>scZcSdagW=Ga?wbsH`MBZkF<KGeWxdGBFiFXotb]WNOY^oUZCyOStCEY<iV\\AUEWvZIe]eea;sLsXfehyYVIqCdgIiwu<]HawdFEI[gHNmHf?ebQXi=i\\?IqiX]MyKccFifRSdZSRQ?VSKD[acB;gRYdXwSn?V^QH;CVQeR>iBJAXC=Sl;rRsHdagJ]h[OL?N`L_dDYvkNkfydcfZO>sFPd;^cHH_l>j^?jL?[^_bJOsFokbN^<G]C?lBXk[^lS`[=X\\hplGXfnhl@pptyy:nyyVxwo\\\\nxogy[gvfYyoNiBfiCaa\\piE@tSQk;yYYwy;riYCsoY[yGIih=yxfYwQeHlCF\\aDLIFQoFcqD;qf\\qFBSV?sRp_C?mHCMc?Mt`ecGAdD?Sl_c`SDdQfF=TM_fDOGCCcJqvBOtBqVCIg`KiJST\\WTY=VBgRAQG[Eyh_uTWgCWBj_rkuWPSFC?C;QXl]gUtOFHQN@m]=uNDs[MJ<yoDLnAHRg=TJlNHMXWumKdSlDPZxV?etmyMAHjL@kgTuLMW:@MXDkRLLWeTmu^q?>QR_;sj=ruKtKeROsBoCHJYiKmdCABdKW^MgOqwRmrrsRCUXQSI<]RWmfO=dpyH==bYcY[qtZ;XEWGkKrvsDwIXpUWcYfAyVUIfk[EsebpgCNIWBOvhoV@eF\\KvLcW@_wLKTHMgfKBV=XT[rB;Vl[C?mV@?GbCHbWV:SdwCs:?iZSc[eeBaT:cF>Se>]brcDjcE>OFsMH^khESfloSQeR>wBDIeNkccABB=FAmSD_cRMcwKG\\GclKTSCTPEt_CT`eRm_VSgsLOdn;GqaXS[C>;hSKwZ_R]Uc]OUSUSEovBmvEgfLoDV_EcKDrgf^eT>wEL]x[ECIGV<]SC[Bf;IZsrv_dn?BUYDR]D>;uFCxbMTHCyc;VLLoshVLLr^hLQ=sShnRqlL<J:HVT\\S^EunYtIaU^@xEMKTIN^PjsMpx`wN]RVlP;ISUdNgHOFIr]LV@=vB`vtHJGIN@DkbAJB`JmisEDoBlPdiUDDUHMvgDJImLLIl`mMDalBtKnlX`XjaPL?HnaLmwMSTIYhtXS=o@lO`LTsxkAEp><mFLtrdNGmP<ymPAlNHs[ALfYTEAj^\\j\\PLUXNsDRW`QLMTaeSO<jsxNRaL:\\YDYQN@lL=SaUtKPvFLP;Ml:dsFLW@qOYLXd<nddMBeqLlxYPKtDPOQY=LysUYxTwRuskTyCEXi`qf\\w_tNmIUxANepOUysqYWxAwvyTh\\yEuSXpul@Xe\\kOYq<qOvtO\\]K<`s``UJ=T=ANK@M?DNNTQN\\tSiQc]MWASZUyLPvDpKNDo^AMCEt\\ALitR_PsJPSfMX;iNHYs\\DJJUX[\\JcHNJhRJ`TS<k\\lJGeP>DuCLPSLj^EmCAlDUnEpY:ApftyqDT[uo?yt\\eX<au_TxEpSituYmTXpuIUpYqYxxY:lX^Hq:ay<]xLessqMApNWIJF=SitsZ@qpiYWPyxmObeV^Pp^AW;TkYXoiaO`PvTpKV`mO`pDujJIW]pxLIKMIp=<Xe<YNysCaK\\XWAhoxtSkUjCHytMvR=SpmxY<xLMwutYB]JZmmlYSj`OKpvamNIasltSHEx]DpEQoCux<XrpMsj@LheuoaqslvVpxbXVCpu@tRs]w?YlrlRAElYhRQhOq@tpXmvhKPAqcitEEXEHx>qr[<k[PRmeYZQWWIWHLP\\XnTmnm`PeeO_Qm?QRYytVYuq\\M?MXk\\JQhMEuRdasc`J^Dsl@KKxNo`voAvM]oV`xOhomxiXvo^ykCIctQfkpxPxaKguWqcZQrMN^rFfAh\\]`t_P_bN`h`bJ>ufpkixy:>_qibegxI@ylywYf`c@krY`MvxkGwuGkUadfQq^Gwv>i@fd[IqVihE^[bnaVoZ^nxp?ofQf_GpvxbqNyc^hcvkdYbCPtO?mBXuiNf`fx?PqpvhOAfNhomvj`iZyAZtwjKwut?f[^[`oiE>c?xvtVm=yhdHerwckXfY^llIqvWf?HtkhuHQ^m?q@ybWV_HxuwgfPGyu^mkggVwkZqpCQ\\tnjA?\\QgmdYnXgv]xxnvboXgSVuCxfbvtRhhdYeE@gu`c^>bZGeVWni?qFHjtHrb>m^IajAvbhhkpnjy[by]OGonPuHynma_m^Z?wm<Xp@A`AOuSWqgiuXxhMXZZPZ=vxe`pgo_dpiefh;qkZXnxHwxPnT?vT_iYO^mPwVyel@pOWfcYvM^xQ_svWd>QxUi[L`sdyhSGdC`jBxhTOqUNZlPiIavyAZqFtaw]gvv\\ie_?ofgrtpklh`tvolxuDOdliwhvy:Fggqdax]wAZyWjdAoYWpdW_x`]]Wvvqd\\ynIYqm^iFWihngFHvoGhF`k>WsYNiH`xhW_L^pF?[<FtAp\\OWoVYmfAnEowF@janm[>go?d?N`hWf`ynC@kYG`lFoopkeYh=^ff?fEF`Iav_`tiQpE@Zh`b>gjYYn;`vCwy:veKadeyahybsqic`]_IcyVcWOuMAqL^jfApDO\\Hfu]q[DvnJ_uUictHf\\VZ<vofqhMAoCns=A_DI\\bomEv_fxiypyJonv^vs`e\\oug?^F>xR^o]?qrpwvimaockx]\\_ukVsrx_xvixyjyEfSSrQixQeIQcwuGoieqsVxeu]]BxKsk=UhcFKSGhGxKdLIyY:@vXUlvdp>UYjTuUXYadslMpFXvTlQ]PMousmhLtIQTunXauv\\qkmKl`m<isSusoUQlHLqpsJ@yy=j<DqOQXVewfLPfUKBIvVYPtqXXyxSPKfiPJHj=QKkdLMDWmXXG`PqQnDqpt`kT@s;@OHPWaxsYMslQXhoyMYuCyedI^pXxhy]?WlsHubOnw`rlF`TVysIoG`cmOws`eIo]JhqthlK`uO?[Bqrm^_AgpAOiq>`Qah`W^:>hIx]LhoP?whqgUQwuYn`v^XX_EGo@XuIIumycM^kQFhNXppynqOqFhnEV]Cofy>v_tuawU;U]aUEEwowd\\wrdyC`sU_WufwIuyu_OiOyWiIcHUEYYWUKGqMbKgEpEs:ibU]y[ErMiuh_wOmE>gF\\ww_siL[XpUycKToqC=Cxbgr;?vesWtwFYUV_[FCau;?Sfar@_EoCxtAhgyXTHmvhWQmJrpXe`KkpxuYmppLDdWwmo;HkZayPpXWLO_UlLlTMTLVTpthNP=TZXWKpkhQoHiWOit<Uvq`Ky]WQqYn<m=aqcxtnpLieWFexB<RA\\QHeVhMokHKQHqsLS\\em_=qwyoYpXL<qmEsLAUieWq<KUMn>ApAum?xTdLSOprw\\PY@r>UxiIUOim_Ixptwp@QRhVY@PhDPMlmvDM_EPx\\yptX@ATdPXCLv=PqDQnGitkaM]yQjDqAxK;IWh]vgPuDItN@NeqKUfep?guqcKxaD@mAW\\iYgVXxXrnMyhMguStbsCMAdhYiiaWlCglESc;F=AgnEfRiFekemaRymgDuiK=ys?Th?rRyB?;fNYgCWwRQR`EiAyvh_wlsudCuL?vmSXEUdIEXZwErou]wCfAe]GwD]h;kFo_SB?xSermmwoeFqqUDYycOct_SZ?SJ]OUAwhupJaL]=VTTsryQ;qUd=rG`qUXp`EonQohxMDLldar@@OmmtxpPShY\\EqUuuIAscLVT=U:TYOis@PWEeooLUCIx=TXDdy@AuEDVCTjb@rd=lDhlUIJdaQrUJYpL`tqO@OHHMEQoDyW=QWrUS;ilwuvhhrULquhKbLjPMJIAky=j<tTt@rOArAlXf<U@eUAQxYyL_AlmxkaUrWyMIPpyXpGpJ=hVllnLUYuuJotRcqWauXylOpDpayRvqlWUj=<r:<RihqMIwOltcaJFqKLdX?XvRDMaYOGHVjDV_UymmvC]W<hrAER`iwfdUhaJ>xnpeKFAYvqlwhPRhWBinBEjmasl@rUEU_IxStO\\@jK\\W_HP`anIIk@tkHeUEEX]Nf=YdehyDynBgkxGdjv]NQs^_ywNkuAZmxlPHpkYsUviwglSonL>^j^_nX^rxZho_xy\\wFvMopIhdrPqvVfFVajidbNqM?ogqbm_lUOwoxdK>y\\ov`vijYpMyppvergjL`^nVkgVc^V_;pl:OZPgbK^\\i_r@Nb@O_aqdmhbX?eHyfZa<YCDYWOGxTmriET=wgx]HSsUlab:]eYEtTWiToGKGT\\KrGuhB]wGgfjuh@?sRGgBwbEExhcGgyDMSCHgvRwx>wsDOCMmEiUu]etpqfe_YKkVhWbVAHpcGEUFoUucMSmSY;Cx[EsJEuy\\myLMYite\\tApywhMYatE]s;ykCllpAthuX\\mrPppPXYuhYETRpevPauCMU\\UnXhtSTtpmTV]neAP=IsElKeyReDlW`q:LV:asx\\tAqTOMy`Mxp=uempHIv\\iYDdQEEY_mTBdT`HvIdpj]UPmxqLrkIS]xO?uRkuklDohykaIPATXeDTuMYEuPopughoupSb@SLHSB`nOxMNuXPet`QM^TrATleTqCpQTaJ^EjA<UPetu=OM`xf`K^\\WTLVAIJuQP@IpFmyTHM\\MMUYM_eytlKmlkIDtKiUEiXoDlm<PMloKHVjYs]hu`TrKMs=MVQpWl<m=aQehTWLYDiU]qWUPQqqPsqxHyrfLv]yr^UOhuPQtrmevCDLW<ruEUc]wyoriXqdqdHWwxygsInnacsOsy_ZkA\\JQwuvsE?vA`uloi;Vh@Xsm_f>_wrpR]R?itdkGq_fV;ugsTMCg=IB>awIsbRAUosEmyxbeFFcFBASReXFmVPuvKeUSgUtOGK[c@mvT_fBMBH;Bf=chCFiAIHKx`[E;[Uy[wNKRhsfdixEcRokHQiE?MFLsWZaXCEeZGHtgXt_WOyBmsrWEfgQXHEHSkWm=hSGfsyfVoeOqRKuNo]opXXpayOet=YOrAWiENeyMnpYMuoLXxeqQBiqoyk\\QkZmon=odeuQ=uYauwDmryLT`q=adOFrqWq_vrIg`ZYi_nZGGmBWf<`bN^dSG^;xrDPmBH]lGdJogvVtfWd;>xSnnlgdJ?]ZfZj>]ZojNwhc`eHPc_HbO@q^Akdg^C_bZPkMNb>^jJIjlV\\<_ZMH_^FjlF]pNbFnwkpew`oyAZ?`nvPnqy\\Ng_hhdYD<wDA?v<sbjcIwYx>YrGSuV_rgaxSEiuQw_]yGyW;SISiB[SF]KB^Sx?wdt_c?CDMCEJwSwwFtGYCWWd?IRmfC_DSiv;?USATWgGqqFIUXg?FHAU@CEg_bOGc^?EpIWcWyGad>uHmMEA?seYeWebu;GBseCySTsR?GxJUsUySruvRsYfQUpYewAylOGlKIrsYI=IPmHw]GKsytEgsqta;ePMdFWtVGSftdjXqq?aT`xnxbMfs<gqi@dFXfX?qBpZRnfAFqfG^Wovch`EppQOdcyfmw_lNn>FmBxlOnsHymvPqgp\\SQ\\GqnvVyEi_NHm]FayAZ@FpyVsynnf_wTQbJgpkp_RNqixhB_lanvgyfZpvAAwPOr?@pNXj<OeEovHYmGwutXwOneFiky`oWakh>jVVehy]?vhs?pihhKN\\TGduif?ih]Pgd_mhamopcfW[@^[QnhPOhaQvKxkVFpeIuiIoXfepwbIwZ[AxWoxw_`gwvaYegnhvwZiQe?n^^Ou^otSf]=wnWWqq`enFwZG`e^nbvuS^bS?abaZx^mRYiPVmkWb`VtNOmAqloWyg?sjpsE@ZANxCIhA`clXs?VqsPjYqlvVebipUPklfc_hh>`^Yf\\W`tpndh_kvop;yuKovn`x[Hm\\VgRHeEPkJolPyuD?_=YecwsFvtWgq`Nq]geF`c=o\\>Y_tfiBAfP`blvjDGtnggfHjK>^FwcKIeYIdeVwontHqc^OpppsGh_TXqIWlRGxhynMqxphge`lf^gEojh>qioxPnw``[n>pGFkTGiahnMHguh`DxtKYmGnpuYr=>aBpZR^]RWiNv`wq`gis@AhMin:p[POpZo^mY\\`Glk^cdAoYI]>Yer>wAfrap`qq_AnnXyhx>iLQuoq`hp]_QpBifqVlBGdYaxrqwkiZ`P`yNkahappyOGi>nbKGsVQaTafq^`FpnCnr_VmqHuUodPahPxta^gsOoupiW`qUQ\\e_l=>vkwi\\XuagcSx`YPxc_]xG]MQuhy^qdW]rDGSX;y;mGPqhn=EMOUfsV=IC\\gT@aXSgCPGX`]StwSO]igMW=?cJGtCIfViWi?wWehD;imme_gT`EbGmF`yfR]C\\MF\\eyScYuuv`kdmgsGKfZcS_IHdcutigOMrJQD:kX_SWlasdcgqwhc]fPoyF=egyx>kbm]E>Sr<GujkXcgup_uCMSN;unAcwQhZ]HSiCGqHwQUxgVQucF_EgydhkV^kRtYvS]HTyV>eeB[rlasFwcO]C\\[imOyHqsGoTKUUrieVOPcasclnohSotRFXKkmtnUN?pX]UtRiQN@oTMUqtRkUVmDLVLxLMWUIwh=N]pJNYkvPktpS@hs`xwRmtdhqSelfyw@LUUEYcanwmQhpY?iMY`SWHTltlcUTjxj>lQEeTThTXyY:LSc]MxEMuho?TYEak;Hk;@r]Uy\\YQgqppdtoylTus[Dv]QlxDsm`N_MP@ElYTryDOgynuXt[lmi`KEpOuLsfQO[hufHX:EPviLw<o^YUDdu\\mxMqUKYOdh`s^gNQaxOtGao_F]p`^JfrX?Z[fmpNvGHiUitAwfpppe`gxpts_v?IuA?oga_WIwJysQnr??gq^`qW_nhu`HpTWp_^pVQy[wbA@d;ixxwelgvq@uio`IivDWZP?ixivixnDhgCie_``IPsO`\\hW^dxdBQ\\GA[=XjuilWvqGSuEiemGJMt`yCqgGjcEFaTTIC<yVrGt@uUjWwmocJaD^aH>Wr<WvkGWpMD`qWLSvrIg:eW@MBgovjIsTaxeqxPOgCGs;?RssVEGt:EcCcEFOBMyh^]seOrHUTgewpEufGuaAc]OUGcUrWtsWH;MEkKfweFb;VHQGgovjGcqyFYigIsEGgWb;C=mwD_cpmXIshUaVX[ElOukygqWwwGcBqfLQe<qhxIWhKwogBC[fmidAuFgqgTEs<cC`svJQd\\[hSADEUikww\\sDuIhpcytOIqQbmgfVqtOycRyGiGgOehD;ipEWmmtJQSHSTmGWf]jhtu[iQUAQh<tTXp?QXpqoUikHpVdUVC@MDQyF\\nCYRj\\kPTNlDmqXmnlTvHoimxxmO:<V`LPyhRIYxk`mp@tUqTImLlySw<w^mLdmRMyM;EpFPupylQipP\\uc]TCYveHJGaUTetgdqkTO\\Tp]eRp]VllSP]RMmMwQQy=tiUoBEXduki`uudxWhmudO\\LM=EQilOeeR``XXAYYlvouKHTmTeNGIPhhWd<QZmtweupTYitPAUSduJSPXpiO@`vS`tFlN`dvditqTMBqW=TS<PPQdnHioPpxKpNeLn]YuuQRPmv<IlN\\rQEnKiVWhohNok_l>ynvV`[G\\AqjdouLIqK_cd>s>QfAQkhAsaOdlGmDPg\\>mAqnXy`@NynykP>nFvqlwthGgl`gdivNxsLP^KHsF^n=QkBfh@HlSgahgcBvbSx^VqpSGihip`Wo>xiFoiewnVoeFwf@a_?YoJYgOAqlfykvaO^lwx\\wqigh`HWtsYkINfnqxGWfhfakGi=Od?IsQHe`An<Gxw>g:PjNFmLQ_B>lranknwMogC>ZbAom^jp>acxp>FmCidK?_;FcVHnKheeO[NQhOWwPoZDOpc_\\LIbNn^>H[nF^:^j[NZ<?g:?lT@c?^vtfpXnb`Yb>`q]Wuuytj@ewxigoob`umFj]_uyOicytovlgYslx_YVtGyoWOthVxpGpay];nxxgv^qdaiytgymfmaVxGVbvp_wIproyVPi`Qpwiq<Nc?g^]QiCH[[@dLDC]V<[Vl=G^ED^Mhfmb:?DTcTKERL]tqOi;Mwk]SIwRlwew=DVGvJ_CmiGVWefac[]dgcdASiI=gKQfMIYXkuYCRZCwYcfYWCdcH@CgmaGTsgmoFtyVq[efubpGtYOYOiw@MVpggbawwmTE_duIvuCTUsFF=DsMW@QDoeTROHV]yWAHyiTIwGruXWiUsQBRGuX=yxmf;=FAObXkrHScaeFSWgFcwyLXDYtqiVjqtBPng\\vCUMWyODam[YU:]jP@RNEl[`nkHRPaSqmL=Yws<TBGf>xcZffuAtlyn[GoEQrKG`l?yLFZsQno@caIr<n_VNfPvcO_liau=og^ydZPc:o\\NIcf_dqYhdhoZalhI\\lar>WgkIfIa_k^dc_[l_b]xnhIr`gk[a`hyvF?pH@`Q@ivydbNgaxnFQjVOcln[Y?k;Gp^XpFhlEwoJpusW^gA`F@jV^udhm<odEghWGhKPZJN\\:n\\kY\\YHrn_uQY_tojRxv_irrqi^P]>?gGAc>glLx^GWiEorTqf<_[Yo\\A>pVPxZYnNagWhpgAv^qb\\OdJhZWHmNP]hirlH_Rppaf^IGdoah>IxbXlXi\\Wnp\\Qk_`ffaqFGueXdCVir>h;Wp[GtKn^_>sHHZwiqCYZb@aRopWaftai_No<Odlp_VWjLXtcaxsih@aaKndRWppH[>WgI^]Pp_\\Q\\Xywf^kCYt=Nnk^i:^gwOwwob>VeHou^>k<O]Rp\\?AuuGlTVvVNZBNtV^veXkFvhjxkeyoKwwDvkB_m^igt`bSH\\\\^elAauGlT_rKFkBnwRWm=V`npqCQ\\F?n`GcyFmmPeuV[Gfl=p_>A^CVugfsjXf\\p^fVeI^peF^HXcdFwUqa^Pe?WoLaZY_[@oaoAfYO_aWqKvrEQ]]iwE`yJipLArkhsFFyfnmO`d^yxSW^cFsoPc?otAQicN`OVbNqxv`_>^mRVZrY_:pqBW\\kWbpV_@@yM^bBqsG>fyAZhvi?ndmWxqWedweB^rUq_lA`tQnn>cZFaR>^?OxS_\\h?_eHh_olXa^`_f^N]S?hXfrHYwfYpa`tVfkmWth^ZFpif_lPXurn\\rF_@?a<pbHVp_OoXNlv^v\\WiQP_affwPbmO`gF]bIZjQtunabnpkppxphWigag]m>lWNscArkHr\\wtN_gmXhen[T`j_qoHWr<VqW?q?`hKgf^Ns<fsr>qkokRNnU?dGH^BIrj_uhW^>g`EQ\\H?m>yfcniSQoufkVxglXeKX^r>cAp[@om@avuPctvpoWZBhkl_lAGaMVyK@bP@wrynbVbGNe:F]u_iX_uQ>chqZr`rx?idy]\\VpvXk]fppXs;fxP>j_NyvPd]_wSn_jHku>mO_[dao>oxDgbUAuOnbkpkV`fR>^A>s`Wpba\\<w`OacoAc<obG?o:xbka]WvdVqwfVp[WcL^aCa`UplrN^UaeF@e`Qj>VbOpbCqsrhg^pc`niSgwY>pV_yUoo^Hfl^it@sMyZ;uWWUC[XT[FJaEZ;t=gvDyRUkgbQGU_wpCH]eY<;RCSY@[UNsxQEu`OrJ]feUeC=HjcuLSEaQBAcH[WB;CytgSpOdA_vEiIIYbWOb@SyfKglot\\?TN;v\\;Imyb=iXJ?udIgSGipaW>gF=_C=ebbqR<;efICMSuiauDWZ@HqLVrZVqY_h]ocXihB?meA`l?[=q]r?x;Go^`m<`kvGeffu>ynx^nHQeT^`A@rxnioAtRQfqomwN]xGuYVsbpf<HyTVhDOrZOfBv^Mwl=>ZVqtb^uMypUIiOWehPfK_lUvdvVhMOwTwvG^q>^n>^joa`HHa`Wj^?\\lGb@F^HIZ=ggIN_=VkINl?IwUYhv@ltPv_O^>GsanxCIbvhrW@pK?]\\I`SghDqhoG[GySwDPYBZQfVadfmyoWdv[CEQUE_BHyCx?GGSvP?rFMXDkeYSi?AdmwVaucF;S`Cd:kIxKFYcDe_sbIuN[Ef=Bq=TJ]GQsUJeXAUf_mHPuFbIFYmT_UXfchBODlKisQHesFe]F^aGNava_V=;uAeg=uBhEv^uRsAvcOTVUSI?d:uDuurWMI_oRrKg^sThCShES>uE^CGl]T>WET_DS_cZoCNCGlETKaVMaVSeRADOl<l?Al^HSlLoFXWBqwgYxh`MrYLAPXoem<uw\\HkIUkjtwe@SitSFIyCYRp\\Y:qUMevAynUQRx<n]muQAMcUUiItr<Ky\\WvQTpuOYQNa`xrirh@oxmS_`k^<s_uVpIRJPRM@N>\\tRhNJdULDN;qJ?mNWmKcIJ?eL@@VbUJOlN:Qke\\NQHh@IZpO[lHg`^jC>[<GZBNb>^J=VBcCBKTMKb>EVgGDpoRscvZeRnKBIECwOx\\ECQaW\\EUEUwsYEUUuAcvruXkSuy;BpgSXWuRsyfoyA?GjwDqIEUwDIAWPqEnCDZ[Fl?Y[mFniiQeeAmtxQwjmXjOuEwRNatMcTMEh^ODLmDO[d`[BCGS[?dJKEKEd<KTKET_uEqsIdmRtaSBSfRyCNMhPKTkaIO;EuASIWgq_DaSRsiIfuyTYGLqhloWjyVqmvuqdAkT:[fBGRLMEMMS<qTiaB]SRRkDTygFwtKoX\\?tOYIA;dkkW=]cY_HsUwmWcEUi\\cs;geOOhSeiF=UJCfBEUHAB@]VxeERwe<UgZcDusGdCT`[VR_rIKc_QeW]d>UxBkdSQTD]VOAwSeDVSVCMCl]wj;rHcxSuUGWe]=Ie_S^YF[AD^IUoaVEAFOYT;aBKYB;kRokVAggsiU<Gt>agOwDBCYFstWqSZmgeqSQkW^QV\\WdVWFa_w:oXgiuxMTqiT_mT>MFBQx;gUQgupkto]b[MSSasSOWuGYfmB<KfKWCX[VxMsuEb:yhGuXVaF:cEjKh?WiPwIPiUSmrOMbs?WfUigacpkdDCfqwE>qbA_i_;ILSU]?DCOhKmCV?uFqd:KGkgeC=S@SbFgdlCUQeUV[ch]XFCuRCG\\IhOGWxqeNWFtqThufc_B>ufJ_rsIxEoEpeVFgF;;SN]B^[tcwfGihQgXmeWN_GKCHKKtjKDxefouhOOD\\GtCoYVgVd[UkgVp?Gf]e<wDQmuDEeFYefAuWsTr_Ro=X\\ms?CIhOxPUEiCGJ[g^MD>]xmiWCqGbeR<]T<sB_Ms`qgvEGKAUI]d:?DRGhH]guMrkKG<iDQ=U@mrLisAKUusi?]feIcj_dv;CH;sl_gxMCgwHKCXcsFKSRZuC[uuNsXQcDmYsfsDMADXAUd=XrGVKMe`=eIKBGAhB[rR]ThevhAwhcFC=C@KI[ysFwEwcUycTNaCDMHliF[Ie\\oX]]c]=TFKBvgdl=UuAiDguF=V\\_C_cCFGiJUiKGyHOetSgKGdVwCI[S:QUXAeC]TG;DrEfFWbukvqUCmAGSMtIGu_cXpsbFgieebMAhO`WZaSiiJ]lMVxJrhOM]RI`J]]T:AVPPTYhs;dJZamOMTWDPK`mMTSOhl:iW\\XsONf\\>]c>ZU@^_Yf:FcH>]<xZ_fkmp\\SOqX@v>irIqja^xAAZqHmLi\\B`vJFfRqhNIecf`IP^HGjA^rlIacvg_ovQgcoOrYoim@sZWhgireOsR`c\\I`FgdJNoMW^sG_dAn<g^eq^@_eMVaTphqYm>of_O``QZrVZ>QwCagRVZ;qbNObR?l[`cbncpvtvg_FXnE^_mQ^nGqGIxCfevw_?`d<Y`bGubPsK_gRVvYPgXQx\\_sCi[vxZ?^g`p`eyhBftt>gFhv^orAH`kVZqx]\\`weNi]pv<^clG`Ia]jQvnhkJ^i@W_`@jFAnmQvu>idg\\Eh`Eax@IdyNwgVxTWaw^ppVnNwb\\qosG\\GacA?jPOsZgdoWaRGeOGhlpfK?luI]Y`q]qu^hbo_wcgkiq\\P`ZAVfIhZk`v:_mk`dqYysfuZPZ?FhtFmrxx[Pcm^utYqdh\\@qeOw^M?skFlhieporLguS?iC@kl>h_^u<VtaxgR>Z;ahJ>kw>oMo\\agg>_vTwr^fm<v[ChwCalqxnFijoNraF[ew^:@rvqdnHw>Hp[F`NOh<GmuVtcNcBPr_VwsG]jOdqHhGw\\U`xFqsF?xKFrsQwCYgTNvr?_H?mBAyJPfDQuiikjQpm^ka>flx^E_mU>`u^lioqqnrTXw>PuM^tFWj[wwUOnBX`:>kKAZj?]\\XddFqUvhmXqCG\\tVeQ?fKoo@whXwfCFiP?vA_]SptIylRnmNax>fp`h^pfgZibkW\\Sx^F`;YyY?wtcXS[T?OhPCvd_bnAs:;sQCIgsI\\qSv_T_]d_=U;aBoCrSORrMR>EGsKtjmgOIWVWDomYWMb^WT>[cIybUQDP]T>=h;Kf>SIbQxf]eMoXtwtn_c_osBibVyxdEcMwsSGwisTL_gvUiAyBhYSJOsBScj?Ed;FmUoRXUKHNn`lBTLcLSalKFlrbmUd]POATCtnRELv<JEXWE]Jm@NQmmBakbexBdTm<K<mvkXKutVhDrLqJhUmD]vb`kGUPA\\SF@XC`q_mLEXxCIk?MLu<YX<Kj`YchTlTMkULcLSKmOl`kSioW\\onmT;huvApFMS<ao_@KlDmGALDAKlTL=o\\G_lS`[ZpjcOpMH^KHdGa[^pj;_\\lVlbns<?qSXs:VZOhd=xtqx[b>tr>i_`xRWkhPv]AqlpdEIaQfepVaMWqth`josWWsUakeWkCY`phcxijoPxcXx_wxSwksAigFac>Z\\>]ZOZEwrN`uUitKFdB_n`Hslfk\\njLWbb>^RInC?lBAolhc<Xm[>l:_ZlVl[bMQCd[d\\kVOafJ[RZ=KJ\\>Hk^<J<EWZ@L><nJFbENgG@tovsR>skneafhqplTIuO__Aarmoe_ifoimAHoi`s:pYwsBiFroWwEyNadrsth]ChkwvSbAmvhcygMvAcGxEUqqy_]gQEr_QGtqwmwsaWsQsEFYIAyS;wGqyufuRPyeO?WL=WXwhZ?DT;D^oV>MB=oF>GcJKEJmF=oNLTL<aJMDO[\\JSak^Ll><SGQk>LSpTRN]SlAXRIO[dr[exrDUGaTOIKFaQ^IKNaUZAYeTmsiTk@l`DSWTTmIlFtKsATeIqKaylyY:LWQiowMQqHLMATS@PE@SHURA<qZaPEURmAWWtp=]K[=pwYSQHsKdMklY;it:LqxqNeMv]PO`<jQ<SedqYhyK\\UNhtSeuDdVR@sraN^qK^eU=dV`EP`lox@W`ulc\\ge^i`Q]lqid>tGNjen^rysagppPdNXkkFjKPheapqNqv?mqnkMAjxI\\SPydVaWArYyuTF^Gh`CqvAovJ@vunqegnlnouGr[gj\\hf]h=ocRIRggTQoSQ_HaSG]MVEEU`yI:]sOiGWqRb?gFcVViUZ?efgs`=FQSi]oh;ktlqb=[fxQvfosiGts]UHyI:gT>CF:CS^?cY;ECSGHWusuSceS\\KT`me`At_Cs?utT?wjKEiWTSYhpEUrWEMaWm_ftqU^;uy;bTkrOqhmydZ]htqrmEDNEFXuHI=sAyI:ACpaBvyv_ORUqs\\WCbKD\\MfL;Ck]gweRAEy[EEMQEoUd[AEJECssxVEx_Wt^aGG=hmsUxwVTYUTeRNQCE]iL_GGWxQau>avcOgxos<YCaUE_KV?miV]H@SVQaWCQTcoTUGgCkd_QBcCWCeW`wY<sU_UR]gXoCDIOwrSSF_S`YFnKGGiu`AEh;R<ODEyTjAs?YYSOTu]h]Oih?SWKtKoYakyGiWG?UdyHhCV[AvlYc[MVYqDtQguAg@ScdCT:qSGMBfIeUOC\\Wi[WyXMVtcVr[DB=T`_GkqYoOxBMYD_cgCdk;r^MCA]tgmhkMV@AD<KTA=DvmtKiU=ghpebpUC^ueN[hB_xR;fEuEdkUyWwKauHiw@MuAKbfmGlIHq?TsaxsUuhMVpmc>_IaSTL;HK_B:EU=UY_?HOWdBYxFIDZ=EZ]uwguwQSGWhtGiUwF\\cX:cFsAcryc?CDWkhQGUSst\\kfL]twebb]gXSSSucOKXFmvFiy_itGqReUhV?S?GXN;IMKhIUiDYcbMy<iBdGtpicR]B_CHWITu]V:shvothtVrTJZMjGUk^QpqPXxXYIQOudnR@KAAkPhSLEkRAnQIPMaT_UNcHQDQtIEmQUNneVsxtsYN;eVYaVpPvw\\qADMsTJ]TO^<xIDXdTTLdQ@MrylnApvbtq`qxdPwm]NvaN:HQL<yhHxJ<ljEpqLjuHKMewAMY<XT:qyq`rvEugeTK<m:`nJHKtPJIIOv]w^hU?TRoIStLM]Do?Ay:EpJqk@=QRiWBLjLYYIdpf=PHLX?]vhenwpMXQQ^`sv@S@moV=LrUO]HYwAugyRVEVehNR=qumtfuP=xY:DqPDPn`TtAjvyvY<thTUm`uiLP`qpC\\sBMSMEl`]vR@xZUohdmPDUU]rFYSP@MOTwsqpO<vBLSKyWKmnxixQXTqmrOHwTmT_ALFiwPLL=uYBTo<imW=jHiSFUVWExHLv>eY<Xo@PwsETtLnEaSCDKqmj\\YqgqpMijT`S_AoCeXCHs<qSUIkiuXATxj@R[AklyK\\UxdtuOiuTXVcEoyhtR`rxAkmyw^ym>`yrdWahOgmnT\\n=lLk\\OBuJFPrPtWkiospnBHSgQxrIqMYUjmTpTMyPOWDpkUj@dskqUPIOFh_GNm>a[r@spwx\\fnVgg[xxPVum^e;Fl>^kxO[Wn]pGuMVaCo>QhAYRjWseWEhiTgYfyAddyulyBkWgjiUU?Y;edK=tfaCBygW_F\\UIoYi_yXUmsoCFvSvMSu\\OSNuV_SUwOhKGThCDiQf^MbRIWigSQaW^cW:Kcl_cBkc[_rACdUIG@SuLwQ>xY:DY>tKuqv`EsGpQVAM:`jgLP]\\MyAotEogmXmelDEPsTj\\lvT]qXeXUUxWwuQHlb?[TVrZA`IqugprcQiSitVNmlfa>xvnIbIQhaWpTYlcN\\>Wv]HdmGkCY]SqgaO]vhkKGkL^l_y]<Xos@qoi_:iky_wPAhyNoVWyAhZ]hyvpb<?u[?`RQqr_a]Hp\\@sMFaHYdlvgrhoPFeopwI^olHnFHbI`qFpd\\PkEH^CO[d^_@hcB^jBafJQjfVm`^jC>lCInJhbF^n@@bSp^L;\\jC@lCMPNHkJbDaBEwTioWn=BKae__cuuyt?upACOSrsCfRsreibhwwPqVSSuf]vwEroQw@qfwaEuOhbuGqirdKqQxne`sRHXIqm[Er]]xxyMdaWQIPw=qaMUsmyeltgpx_ey]Ey]UoYdW^LT_anQhMbmN=q^MF>?dZSc[_DS_cDSc[_TL[fCMD_mfG;DZaTLeCN=C<;L>:::@n@iUnuupTrt<m=DkALMUqUOpxTER^]sj]ss\\ruqLLqlqQM``pE@P>Dn[AP>Dn:NB:Z>NmJFj[^`Z:abJOrHUHciw>=vYSr<aoqQNd]gJY^`VSguO[vZqSlwglEW<KT<MtjKFr=BrcfWiyJQH[KD>;FlSbL_hJgWDOx?qBKeGX;RUActqGQGCReH^ECmIVQ[FbMHwqi_]c;]byotk?ye?dcYRxIV?=E<KCUgiIAdtCh^MTIQigGyhEc?KWZShLoSamdJSBhaXh=Xs[R:yBUqbEMRpWds_Do[YIGGiwuTUd<ohNEFNsHJKT`AbB[Ev;iIOSiqyPiISQBccc:oiRkrIOuo?TPOd_UU\\CWo?BkGfWcewqVRSDG_iO[fbQgqUsAUYTyI:[CyeB@SUuufiuEcODRcsJkuK]wT=sPmrXOvWiCkcHSAs:=Fn]sBoHeUeg[dcoSPsdJAfIuX^uVn[wrkR]]s\\WsHUV_qx^GWpYBEiRn[rjqXmQUBqdL]eb=FOkdEGFBMWBEdCcd;WxK[eU]vW;EFKX;;G[crWctp?S=oEQCUSirBmwOqsHEYDYHNaBaCTGMElUCSQSTSTbaXsudIUDSKRrkFYiVVQRm?FKUF:gS^aiD_I?eDH?xukcm_Dv[g:As[YYQiCF_WNOElsRwItNQG<=D_KCqEid;SRgYjwgdCIdGs;Wd>=SauVP?d<qTEkvp;tKgKIuxOYp<UPW\\Q]AOdutJTjlPQqLn:Em?ujBHRWTnHUwM]qVHxluyt]t<qpNTNBlW[lJkEOslqblY?ptXpsgisKhMl]jAiWFTR>eOninNdSUDkDUxoiJC=Vjlv=PjJMTlLt<QK_ew^Yj_hmr`Vm`OSYur\\lvmtJljk\\J=xj`mpJTjxLsgUjT`XLTJ=@N^mon`wh=ODITJXPSHYDETqQUBqtLEm<iKEEwL\\kAAxPuuOQuMMQr@R>qXcyOmeVwEK_YPpTQI@NSPLliNCIqL\\pJejN@LT<<K:CB[[pJ:::\\ltqkPiSNeRj=NAEQyhLRLqG\\MFyd?@qHQfd>]VP^`gvEyg>ohji\\:A`ENnb?ef?lT@\\^n>MR<=g:?DT;D^oF>DMn<nCENB\\J[<K>:::::::::::::::::::::::::::::::rYyYp5:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCImUy0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIlITQjRiotJSlDSElMRFJFTkc2Ig==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=