Solution: To solve for $\mathbf{v}$, we use the cross product equation $\mathbf{v} \times \mathbf{w} = \mathbf{p}$. Let $\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}$. The cross product $\mathbf{v} \times \mathbf{w}$ is calculated as $\begin{pmatrix} v_2 \cdot 3 - v_3 \cdot (-1) \\ v_3 \cdot 2 - v_1 \cdot 3 \\ v_1 \cdot (-1) - v_2 \cdot 2 \end{pmatrix} = \begin{pmatrix} 3v_2 + v_3 \\ 2v_3 - 3v_1 \\ -v_1 - 2v_2 \end{pmatrix}$. Setting this equal to $\mathbf{p} = \begin{pmatrix} 5 \\ 0 \\ -2 \end{pmatrix}$, we get the system:

Wed, 06 May 2026 11:55:48 +0000

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