Question

The area of parallelogram whose adjacent sides are $\hat{i}+\hat{k}and2\hat{i}+\hat{j}+\hat{k}$ is

• A.
• B.
• C. 3 sq. units
• D. 4 sq. units

Answer 1

The correct option is B

$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 0& 1\\ 2& 1& 1\end{array}\right|=\hat{i}(1-)-\hat{j}(-1)+\hat{k}\left(1\right)=-\hat{i}-\hat{j}+\hat{k}\text{area of parallelogram}=|-\hat{i}+\hat{j}+\hat{k}|=\sqrt{3}sq.mts.$