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Geometria Analítica e Álgebra Linear - MGA001
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Questão

Em álgebra linear vetorial, os produtos escalar, vetorial e triplo em \mathbb{R}^{3} medem projeção, área perpendicular e volume assinado, respectivamente, com [\mathbf{u},\mathbf{v},\mathbf{w}]=\det\begin{pmatrix}u_1&v_1&w_1\\u_2&v_2&w_2\\u_3&v_3&w_3\end{pmatrix}.

Dadas \mathbf{u}=\begin{pmatrix}1\\2\\3\end{pmatrix}, \mathbf{v}=\begin{pmatrix}4\\5\\6\end{pmatrix}, \mathbf{w}=\begin{pmatrix}7\\8\\9\end{pmatrix}. Calcule [\mathbf{u},\mathbf{v},\mathbf{w}].
A) 0
B) 32
C) ( − 3 , 6 , − 3 )
D) u × v + w
E) 1 ⋅ 4 + 2 ⋅ 5 + 3 ⋅ 6
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