Question
Find the area of the parallelogram with $\mathbf{a}=-\mathbf{i}+\mathbf{j}-3 \mathbf{k}$ and $\mathbf{b}=4 \mathbf{i}+2 \mathbf{j}-4 \mathbf{k}$ as the adjacent sides.
Step 1
The cross product of two vectors $\mathbf{a}$ and $\mathbf{b}$ is given by $\mathbf{a} \times \mathbf{b} = (a_2b_3 - a_3b_2)\mathbf{i} - (a_1b_3 - a_3b_1)\mathbf{j} + (a_1b_2 - a_2b_1)\mathbf{k}$. Show more…
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