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  4. The area of a parallelogram whose adjacent sides are 3 hati- hatj- hatk hati+ hatj+2 hatk is.... sq. units.

Q. The area of a parallelogram whose adjacent sides are $3 \hat{i}-\hat{j}-\hat{k}\, \&\,\hat{i}+\hat{j}+2 \hat{k}$ is.... sq. units.

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Solution:

$\vec{a} \times \vec{b}=\begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\ 3 & -1 & -1 \\ 1 & 1 & 2\end{vmatrix}=-\hat{i}-7 \hat{j}+4 \hat{k}$
$A=|\vec{a} \times \vec{b}| \sqrt{1+49+16}$
$=\sqrt{66}$

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