[justify][b][code][/code]OBJETIVO: [/b]Verificar os cálculos do produto vetorial e misto. Observar as interpretações geométricas da área do paralelogramo, do volume do paralelepípedo, prisma e tetraedro. [br][br][b]BREVE TEORIA: [/b]Dado dois vetores [math]\vec{v}[/math] e [math]\vec{w}[/math], no espaço, sabemos que seu produto vetorial [math]\vec{v}\times\vec{w}[/math] é um vetor resultante também no espaço. Desse modo, dado um terceiro vetor [math]\vec{u}[/math], pode-se fazer o produto escalar de [math]\vec{u}[/math] por [math]\vec{v}\times\vec{w}[/math], obtendo-se um número real. Esse produto é dito como[b] produto misto[/b] dos vetores [math]\vec{u}[/math], [math]\vec{v}[/math] e [math]\vec{w}[/math], que é representado por [math]\vec{u}\cdot\left(\vec{v}\times\vec{w}\right)[/math] , essa expressão é o desenvolvimento do seguinte determinante:[br][br][img]data:image/png;base64,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[/img][br]No applet também é representado a interpretação geométrica do produto misto, a saber [math]|\vec{u}\cdot\left(\vec{v}\times\vec{w}\right)|[/math]. Esse valor representa o volume do paralelepípedo determinado por [math]\vec{u}[/math], [math]\vec{v}[/math] e [math]\vec{w}[/math].[/justify][b]ATIVIDADE: [/b]Selecionar as caixas da direita para visualizar os produtos entre os vetores.[br][br]