If $\vec a$ and $\vec b$ are two unit vectors inclined at an angle θ such that $|\vec a +\vec b|<1$, then
Answer & explanation
Correct answer: option 1
We have,
$|\vec a +\vec b|<1$
$⇒|\vec a +\vec b|^2<1$
$⇒|\vec a|^2 +|\vec b|^2+2(\vec a.\vec b)<1$
$⇒1+1+2\cos θ<1$
$⇒2+2\cos θ<1⇒\cos θ<-\frac{1}{2}⇒\frac{2π}{3}<θ<\frac{4π}{3}$