Question

If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{2\pi }{3}$ and the projection of $\overrightarrow{a}$ in the direction of $\overrightarrow{b}$ is $-2$, then $|\overrightarrow{a}|=$

• A. 2
• B. 4
• C. 1
• D. 3

Answer 1

The correct option is B 4

As the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is$\theta =\frac{2\pi }{3}$ and $\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}=-2$
$\Rightarrow \frac{|\overrightarrow{a}||\overrightarrow{b}|\cos \theta }{|\overrightarrow{b}|}=-2\Rightarrow |\overrightarrow{a}|\cos \frac{2\pi }{3}=-2\Rightarrow |\overrightarrow{a}|\times \frac{-1}{2}=-2\Rightarrow |\overrightarrow{a}|=4$