Question

Find out the area of the parallelogram whose adjacent sides are $\hat{i}+\hat{j}+3\hat{k}$ and $-\hat{i}-2\hat{j}+\hat{k}$

Answer 1

Area of a parallelogram whose adjacent sides are given by $\overrightarrow{a}$ and $\overrightarrow{b}$

is given by :

Area = $|\overrightarrow{a}\times \overrightarrow{b}|$

According to question ,

$\overrightarrow{a}$ = $\hat{i}+\hat{j}+3\hat{k}$

$\overrightarrow{b}$ = $-\hat{i}-2\hat{j}+\hat{k}$

Therefore, area of the parallelogram is :

Area = $|\overrightarrow{a}\times \overrightarrow{b}|$

= $|7\hat{i}-4\hat{j}-\hat{k}|$

= $\sqrt{66}$ square units .