Question

If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$ then angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${90}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

Answer: (C)

${90}^{\circ }$

$|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}+\overrightarrow{b}|$
$\Rightarrow |\overrightarrow{a}+\overrightarrow{b}{|}^2=|\overrightarrow{a}-\overrightarrow{b}{|}^2$
$\Rightarrow |a{|}^2+|b{|}^2+2\overrightarrow{a}.\overrightarrow{b}cos\theta$
$=|a{|}^2+|b{|}^2-2\overrightarrow{a}.\overrightarrow{b}cos\theta$
$\overrightarrow{a}.\overrightarrow{b}=0$
$\cos \theta =0$
$\theta ={90}^o$