Question

If $2\vec {a}$.$\vec {b}= \vec |a|. \vec |b|$ then the angle between $\vec{a}$ and $\vec{b} $ is

• A. $30 ^{\circ} $
• B. $0 ^{\circ }$
• C. $90 ^{\circ} $
• D. $60 ^{\circ} $

Answer 1

Answer: (D)

Given $2 \vec{a} . \vec{b} = \left|\vec{a}\right| \left|\vec{b}\right|$
We know that, if $\theta$ is angle between two non - zero vectors $\vec{a}, \vec{b}$, then
$ \Rightarrow 2 \left|\vec{a}\right| \left|\vec{b}\right| \cos\theta = \left|\vec{a}\right| \left|\vec{b}\right|$
$ \Rightarrow \cos\theta = \frac{1}{2} $
$ \therefore \Rightarrow \theta = 60^{\circ}$