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)

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