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Home » \beginpmatrix 1 \\ -2 \\ 3 \endpmatrix \times \beginpmatrix 4 \\ 0 \\ -1 \endpmatrix = \beginvmatrix \mathbfi & \mathbfj & \mathbfk \\ 1 & -2 & 3 \\ 4 & 0 & -1 \endvmatrix - AMAZONAWS

\beginpmatrix 1 \\ -2 \\ 3 \endpmatrix \times \beginpmatrix 4 \\ 0 \\ -1 \endpmatrix = \beginvmatrix \mathbfi & \mathbfj & \mathbfk \\ 1 & -2 & 3 \\ 4 & 0 & -1 \endvmatrix - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
\begin{pmatrix} 1 \\ -2 \\ 3 \end{pmatrix} \times \begin{pmatrix} 4 \\ 0 \\ -1 \end{pmatrix} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -2 & 3 \\ 4 & 0 & -1 \end{vmatrix}

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📌 The final answer is \boxed{-6}.Question: An anthropologist models the migration paths of two ancient tribes as vectors $\vec{u} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$ and $\vec{v} = \begin{pmatrix} -2 \\ 4 \\ 1 \end{pmatrix}$. There exists a vector $\vec{w} = \begin{pmatrix} a \\ b \\ c \end{pmatrix}$ such that $\vec{w} = 2\vec{u} - 3\vec{v}$. Find $\vec{w}$.
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