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If $\mathbf{a} \cdot \mathbf{i}=4$, then $(\mathbf{a} \times \mathbf{j}) \cdot(2 \mathbf{j}-3 \mathbf{k})=$
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Verified Answer
The correct answer is:
-12
$\begin{aligned}
& (\mathbf{a} \times \mathbf{j}) \cdot(2 \mathbf{j}-3 \mathbf{k})=\mathbf{a}\{\mathbf{j} \times(2 \mathbf{j}-3 \mathbf{k})\} \\
& =\mathbf{a} \cdot\{-3(\mathbf{j} \times \mathbf{k})\}=-3(\mathbf{a} \cdot \mathbf{i})=-12
\end{aligned}$
& (\mathbf{a} \times \mathbf{j}) \cdot(2 \mathbf{j}-3 \mathbf{k})=\mathbf{a}\{\mathbf{j} \times(2 \mathbf{j}-3 \mathbf{k})\} \\
& =\mathbf{a} \cdot\{-3(\mathbf{j} \times \mathbf{k})\}=-3(\mathbf{a} \cdot \mathbf{i})=-12
\end{aligned}$
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