Vectors - Cross Product - Highlighted Algebraic Formula and Value Matrix to Highlighted Matrix

Question

Select the matrix that highlights the products for the indicated component of the cross product. Green marks the positive product; red marks the negative product.

$$\begin{gathered}\vec{u}	imes\vec{v}=\left[\, (u_{2}v_{3}-u_{3}v_{2}),\ \fcolorbox{#1b7f3b}{#e6f7ec}{$-(u_{1}v_{3}-u_{3}v_{1})$},\ (u_{1}v_{2}-u_{2}v_{1}) \,ight]\\vec{u}	imes\vec{v}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\ 1&-1&-2\ -3&-3&1\end{vmatrix}\end{gathered}$$

Accepted Answer

$$\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\ \fcolorbox{#1b7f3b}{#e6f7ec}{$1$}&-1&\fcolorbox{#b91c1c}{#fde8e8}{$-2$}\ \fcolorbox{#b91c1c}{#fde8e8}{$-3$}&-3&\fcolorbox{#1b7f3b}{#e6f7ec}{$1$}\end{vmatrix}$$

Answer

$$\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\ \fcolorbox{#b91c1c}{#fde8e8}{$1$}&-1&\fcolorbox{#1b7f3b}{#e6f7ec}{$-2$}\ \fcolorbox{#1b7f3b}{#e6f7ec}{$-3$}&-3&\fcolorbox{#b91c1c}{#fde8e8}{$1$}\end{vmatrix}$$

Answer

$$\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\ \fcolorbox{#1b7f3b}{#e6f7ec}{$1$}&\fcolorbox{#b91c1c}{#fde8e8}{$-1$}&-2\ \fcolorbox{#b91c1c}{#fde8e8}{$-3$}&\fcolorbox{#1b7f3b}{#e6f7ec}{$-3$}&1\end{vmatrix}$$

Answer

$$\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\ 1&\fcolorbox{#1b7f3b}{#e6f7ec}{$-1$}&\fcolorbox{#b91c1c}{#fde8e8}{$-2$}\ -3&\fcolorbox{#b91c1c}{#fde8e8}{$-3$}&\fcolorbox{#1b7f3b}{#e6f7ec}{$1$}\end{vmatrix}$$

Practice: Vectors - Cross Product - Highlighted Algebraic Formula and Value Matrix to Highlighted Matrix

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Vectors - Cross Product - Highlighted Algebraic Formula and Value Matrix to Highlighted Matrix

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