Cap\303\255tulo 4: Produto Escalar e Produto VetorialO produto escalar e o produto vetorial s\303\243o opera\303\247\303\265es importantes com vetores. Vale a pena apontar a sintaxe para trabalhar essas opera\303\247\303\265es com o Maple.
(Voc\303\252 pode usar o Maple como outra maneira de verificar seu trabalho.)
Primeiro, definimos um monte de vetores:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSI7RidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y0Ri8=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Os comandos para produto escalar e produto vetorial fazem parte do pacote de \303\241lgebra linear. A sintaxe \303\251: linalg[dotprod](vetor1, vetor2);
linalg[crossprod](vetor1, vetor2); 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Uma sintaxe alternativa \303\251 usar o comando "with (linalg):" para carregar o pacote de \303\241lgebra linear e usar a forma abreviada do comando. Dessa forma, o pacote precisa ser carregado apenas uma vez em uma sess\303\243o do Maple.
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=