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In Problems 15-22, find (a) $\mathbf{v} \times \mathbf{w},($ b) $\mathbf{w} \times \mathbf{v},(c) \mathbf{w} \times \mathbf{w}$, and (d) $\mathbf{v} \times \mathbf{v}$. $\begin{aligned} \mathbf{v} & =\mathbf{i}-4 \mathbf{j}+2 \mathbf{k} \\ \mathbf{w} & =3 \mathbf{i}+2 \mathbf{j}+\mathbf{k}\end{aligned}$

   In Problems 15-22, find (a) $\mathbf{v} \times \mathbf{w},($ b) $\mathbf{w} \times \mathbf{v},(c) \mathbf{w} \times \mathbf{w}$, and (d) $\mathbf{v} \times \mathbf{v}$.
 $\begin{aligned} \mathbf{v} & =\mathbf{i}-4 \mathbf{j}+2 \mathbf{k} \\ \mathbf{w} & =3 \mathbf{i}+2 \mathbf{j}+\mathbf{k}\end{aligned}$

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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 18

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Step 1

To find the cross product $\mathbf{v} \times \mathbf{w}$, use the determinant formula: \[ \mathbf{v} \times \mathbf{w} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -4 & 2 \\ 3 & 2 & 1 \end{vmatrix} \] Expand this determinant: \[ \mathbf{v} \times Show more…

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In Problems 15-22, find (a) $\mathbf{v} \times \mathbf{w},($ b) $\mathbf{w} \times \mathbf{v},(c) \mathbf{w} \times \mathbf{w}$, and (d) $\mathbf{v} \times \mathbf{v}$. $\begin{aligned} \mathbf{v} & =\mathbf{i}-4 \mathbf{j}+2 \mathbf{k} \\ \mathbf{w} & =3 \mathbf{i}+2 \mathbf{j}+\mathbf{k}\end{aligned}$

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