Question

The area of the parallelogram whose adjacent sides are $3\hat{i}+2\hat{j}+\hat{k}$ and $\hat{j}+2\hat{k}$ is

• A. $3\sqrt{6}$
• B. $4$
• C. $54$
• D. $\frac{3\sqrt{6}}{2}$

Answer 1

The correct option is A $3\sqrt{6}$

Required area is the magnitude of the cross product of the two vectors.
$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 2& 1\\ 0& 1& 2\end{array}\right|=3\hat{i}-6\hat{j}+3\hat{k}$
$\text{Required Area}=\sqrt{3^2+(-6{)}^2+3^2}=\sqrt{54}=3\sqrt{6}$