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