Question

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$. What is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ ?

• A. $0^o$
• B. ${90}^o$
• C. ${60}^o$
• D. ${180}^o$

Answer 1

The correct option is B ${90}^o$

$|\overrightarrow{a}+\overrightarrow{b}|=a^2+b^2+2ab\cos \theta$

$|\overrightarrow{a}-\overrightarrow{b}|=a^2+b^2+2ab\cos (\Pi -\theta )$

$\Rightarrow |\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|\Rightarrow a^2+b^2+2ab\cos \theta =a^2+b^2-2ab\cos \theta$

$\Rightarrow 4abcos\theta =0$

$\Rightarrow cos\theta =0$ or $\theta ={90}^0$