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 $=\| a \times b \| $
$\begin{Vmatrix}\hat{i}&\hat{j}&\hat{k}\\ 1&0&1\\ 2&1&0\end{Vmatrix}$
$=|\hat{ i }(0-1)-\hat{ j }(1-2)+\hat{ k }(1-0)|$
$=|-\hat{ i }+\hat{ j }+\hat{ k }|$
$=\sqrt{(-1)^{2}+(1)^{2}+(1)^{2}}= \sqrt{3}$