Physics - Vectors Question with Solution | TestHub

The area of the parallelogram formed by vectors $\vec{P}$ and $\vec{Q}$ is given by $|\vec{P}\times \vec{Q}|$.

$\vec{P}\times \vec{Q}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& -1& 5\\ 3& -2& 4\end{array}\right|$

$=\hat{i}((-1)(4)-(5)(-2))-\hat{j}((2)(4)-(5)(3))+\hat{k}((2)(-2)-(-1)(3))$

$=\hat{i}(-4+10)-\hat{j}(8-15)+\hat{k}(-4+3)$

$=6\hat{i}+7\hat{j}-\hat{k}$

The magnitude of the cross product is:

$|\vec{P}\times \vec{Q}|=\sqrt{6^2+7^2+(-1{)}^2}$

$=\sqrt{36+49+1}=\sqrt{86}$

Answer: $\sqrt{86}$