Question

If $\overline{a},\overline{b},\overline{c}$ are unit vectors satisfying the relation $\overline{a}+\overline{b}+\sqrt{3}\overline{c}=0$, then the angle between $\overline{a}$ and $\overline{b}$ is

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is C $\frac{\pi }{3}$

Rearranging the given equation:

$\overline{a}+\overline{b}=-\sqrt{3}\overline{c}$

Squaring the modulus of both the sides:
${|\overline{a}+\overline{b}|}^2=3{\left|\overline{c}\right|}^2$

${\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2+2\overline{a}.\overline{b}=3$

Since, $\overline{a},\overline{b},\overline{c}$ are unit vectors, $|a|=|b|=|c|=1$
$2\cos \theta =1\Rightarrow \cos \theta =\frac{1}{2}$
$\theta =\frac{\pi }{3}$