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Prove the following

Question:

If $\vec{A}=2 \vec{\imath}+3 \vec{\jmath}+4 \vec{k}$ and $\vec{B}=4 \vec{\imath}+3 \vec{\jmath}+2 \vec{k}$, find $\vec{A} \times \vec{B}$.

Solution:

$\mathrm{A}=2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k}, \mathrm{B}=4 \mathbf{i}+3 \mathbf{j}+2 \mathbf{k}$

$\mathbf{A} \times \mathbf{B}=[i j k 234432]=-6 \mathbf{i}+12 \mathbf{j}-6 \mathbf{k}$

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