Question

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

• A. $3\sqrt{10}$
• B. $4\sqrt{10}$
• C. $\sqrt{10}$
• D. $2\sqrt{10}$

Answer 1

Answer: (D)

$2\sqrt{10}$

Area of Parallelogram $=|\overrightarrow{a}\times \overrightarrow{b}|$
$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 2& 1\\ 3& 0& 1\end{array}\right|=2\hat{i}-6\hat{k}$
$|\overrightarrow{a}\times \overrightarrow{b}|=2\sqrt{10}=area$