Question

The angle between two adjacent sides $\overrightarrow{a}$ and $\overrightarrow{b}$ of a parallelogram is $\frac{\pi }{6}$. If $\overrightarrow{a}=(2,2,-1)$ and $|\overrightarrow{b}|=2|\overrightarrow{a}|$, then area of this parallelogram is

• A. $9$
• B. $18$
• C. $\frac{9}{2}$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $9$


$|\overrightarrow{a}|=\sqrt{4+4+1}=3$

Area of the parallelogram is given by
$|\overrightarrow{a}\times \overrightarrow{b}|$
$=|\overrightarrow{a}||\overrightarrow{b}|\sin \left(\frac{\pi }{6}\right)$
$=3\times 2\times 3\times \frac{1}{2}=9$