Question

The area of a parallelogram whose two adjacent sides are represented by the vectors $3\hat{i}-\hat{k}$ nad $\hat{i}+2\hat{j}$ is

• A. $\frac{\sqrt{17}}{2}$
• B. $\frac{\sqrt{14}}{2}$
• C. $\sqrt{41}$
• D. $\frac{\sqrt{7}}{2}$

Answer 1

The correct option is C $\sqrt{41}$

The area of the parallelogram is given by $=|\overrightarrow{AB}\times \overrightarrow{AD}|$

Here, we are given adjacent sides and so

$\overrightarrow{AB}\times \overrightarrow{AD}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 0& -1\\ 1& 2& 0\end{array}\right|=2\hat{i}-\hat{j}+6\hat{k}$

Hence, the required area is $=|2\hat{i}-\hat{j}+6\hat{k}|=\sqrt{41}$