Question

If $\overrightarrow{A}$ = $3\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{B}$ = $2\hat{i}-2\hat{j}+4\hat{k}$ then find the value of $|\overrightarrow{A}\times \overrightarrow{B}|$.

• A.
• B.
• C. 194
• D.

Answer 1

The correct option is D

$\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 1& 2\\ 2& -2& 4\end{array}\right|=(1\times 4-2\times -2)\hat{i}+(2\times 2-4\times 3)\hat{j}+(3\times -2-1\times 2)\hat{k}=-8\hat{j}-8\hat{k}\therefore Magnitudeof\overrightarrow{A}\times \overrightarrow{B}=|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{(-8{)}^2+(-8{)}^2}=8\sqrt{2}$