Question

If $2\vec{a}$.$\vec{b}=\overrightarrow{|}a|.\overrightarrow{|}b|$ 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
$\Rightarrow 2\left|\vec{a}\right|\left|\vec{b}\right|\cos \theta =\left|\vec{a}\right|\left|\vec{b}\right|$
$\Rightarrow \cos \theta =\frac{1}{2}$
$\therefore \Rightarrow \theta =60^{\circ }$