Question

Calculate the area of a parallelogram formed by vectors$.$
$\overrightarrow{A}=3\hat{i}+2\hat{j}$ and $\overrightarrow{B}=-3\hat{i}+7\hat{j}$

Answer 1

$\text{Step 1: Area of parallelogram}$

Area of parallelogram formed by $\overrightarrow{A}$ and $\overrightarrow{B}$ is given by

$Area=|\overrightarrow{A}\times \overrightarrow{B}|$

$\text{Step 2: Cross -Product}$

$\overrightarrow{A}\times \overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 2& 0\\ -3& 7& 0\end{array}\right|$

$=\hat{i}(0-0)-\hat{j}(0-0)+k(21+6)=27\hat{k}$

$\therefore |\overrightarrow{A}\times \overrightarrow{B}|=27$ sq.unit

Hence the area of a parallelogram is $27$ sq unit