Question

The sides of a parallelogram are along $\overline{a}=\hat{i}+2\hat{j}+\hat{k}$ and $\overline{b}=2\hat{i}+\hat{j}$, then the area of the parallelogram

• A. $\sqrt{14}$
• B. $\frac{1}{2}\sqrt{14}$
• C. $2\sqrt{14}$
• D. $\frac{\sqrt{14}}{3}$

Answer 1

The correct option is A $\sqrt{14}$

$\Rightarrow \text{Area}=\left|\right(\hat{i}+2\hat{j}+\hat{k})\times (2\hat{i}+\hat{j}\left)\right|$
$\Rightarrow \text{Area}=|\hat{k}-4\hat{k}+2\hat{j}-\hat{i}|$
$\Rightarrow \text{Area}=|-\hat{i}+2\hat{j}-3\hat{k}|$
$\Rightarrow \text{Area}=\sqrt{14}$