Question

The area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}$ = $\hat{i}+2\hat{j}+3\hat{k}$ and $\overrightarrow{B}$ = $2\hat{i}-3\hat{j}+\hat{k}$ is.

• A. $\sqrt[4]{4195}$sq unit
• B. 0.0
• C. 195 sq unit
• D. $\sqrt{195}$sq unit

Answer 1

The correct option is D $\sqrt{195}$sq unit

We know that the area of the parallelogram is equal to the magnitude of the cross product of given vectors.

Now,
$\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 2& 3\\ 2& -3& 1\end{array}\right|=\hat{i}(2+9)+\hat{j}(6-1)+\hat{k}(-3-4)=11\hat{i}+5\hat{j}-7\hat{k}Soareaofparallelogram:|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{{11}^2+5^2+(-7{)}^2}=\sqrt{195}sq.unit$