Question

Area of parallelogram whose adjacent sides are $\overrightarrow{a}=\hat{i}-\hat{j}+3\hat{k}$ and$\overrightarrow{b}=2\hat{i}-7\hat{j}+\hat{k}$ is

• A. $15\sqrt{2}$ sq. units
• B. $20$ sq. units
• C. $25\sqrt{14}$ sq. units
• D. $30$ sq. units

Answer 1

The correct option is A $15\sqrt{2}$ sq. units

We know, area of parallelogram whose adjacent sides are $\overrightarrow{a},\overrightarrow{b}=|\overrightarrow{a}\times \overrightarrow{b}|$
$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -1& 3\\ 2& -7& 1\end{array}\right|$
$=20\hat{i}+5\hat{j}-5\hat{k}$
$\Rightarrow |\overrightarrow{a}\times \overrightarrow{b}|=|20\hat{i}+5\hat{j}-5\hat{k}|=5\sqrt{18}=15\sqrt{2}\text{sq. units}$