Angle between vectors $\vec a$ and $\vec b$, where $\vec a, \vec b$ and $\vec c$ are unit vectors satisfying $\vec a+ \vec b + \sqrt{3}\vec c =\vec 0$, is
Answer & explanation
Correct answer: option 3
We have,
$\vec a+ \vec b + \sqrt{3}\vec c =\vec 0$
$⇒\vec a+ \vec b=-\sqrt{3}\vec c$
$⇒|\vec a+ \vec b|=\sqrt{3}|\vec c|$
$⇒|\vec a+ \vec b|^2=3|\vec c|^2$
$⇒|\vec a|^2+|\vec b|^2+2|\vec a||\vec b|\cos θ=3|\vec c|^2$,
where θ is the angle between $\vec a$ and $\vec b$
$⇒1+1+2\cos θ=3⇒\cos θ=\frac{1}{2}⇒θ=\frac{π}{3}$