Question

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

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

Answer 1

Answer: (B)

Let adjacent sides of a parallelogram are
$a=\hat{i}+\hat{k}$ and $b=2\hat{i}+\hat{j}+\hat{k}$
$\therefore$ Area of parallelogram $=\Vert a\times b\Vert$
$\Vert \begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 0& 1\\ 2& 1& 0\end{array}\Vert$
$=|\hat{i}(0-1)-\hat{j}(1-2)+\hat{k}(1-0)|$
$=|-\hat{i}+\hat{j}+\hat{k}|$
$=\sqrt{(-1{)}^2+(1{)}^2+(1{)}^2}=\sqrt{3}$