Question

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

• A. 2
• B. 4
• C. 1
• D. 3

Answer 1

Answer: (B)

$\theta=\frac{2\pi}{3}$
$\Rightarrow \, \frac{\vec{a}.\vec{b}}{\left|\vec{b}\right|}=-2$
$\Rightarrow \, \frac{\left|\vec{a}\right|\left|\vec{b}\right|cos \theta}{\left|\vec{b}\right|}=-2$
$\Rightarrow \, \left|\vec{a}\right| cos \frac{2\pi}{3}=-2 $
$\Rightarrow \, \left|\vec{a}\right|\times-\frac{1}{2}=-2 $
$\Rightarrow \left|\vec{a}\right|=4$