Question

If $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}|=|\overrightarrow{B}|$ then angle between $A$ and $B$ will be:

• A. ${90}^o$
• B. ${120}^o$
• C. $0^o$
• D. ${60}^o$

Answer 1

The correct option is B ${120}^o$

Resultant of two vectors is given by, $|\overrightarrow{A}+\overrightarrow{B}|=\sqrt{|A{|}^2+|B{|}^2+2|A||B|\cos \theta }$

where $\theta$ is angle between them.

Given,

$|\overrightarrow{A}+\overrightarrow{B}|=\sqrt{|\overrightarrow{A}{|}^2+|\overrightarrow{B}{|}^2+2|\overrightarrow{A}||\overrightarrow{B}|\cos \theta }=|\overrightarrow{A}|$

Squaring on both side and putting $|\overrightarrow{A}|=|\overrightarrow{B}|$

$|\overrightarrow{A}{|}^2+|\overrightarrow{A}{|}^2+2|\overrightarrow{A}||\overrightarrow{A}|\cos \theta =|\overrightarrow{A}{|}^2$

$2|\overrightarrow{A}{|}^2\cos \theta =-|\overrightarrow{A}{|}^2$

$\cos \theta =-\frac{1}{2}$

$\theta ={120}^o$