Question

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. The angle between the two vectors will be

• A. $0^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${45}^o$

Answer 1

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

$|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$

$⟹$ ${|\overrightarrow{A}+\overrightarrow{B}|}^2={|\overrightarrow{A}-\overrightarrow{B}|}^2$

$⟹A^2+B^2+2\overrightarrow{A}.\overrightarrow{B}=A^2+B^2-2\overrightarrow{A}.\overrightarrow{B}$

$⟹\overrightarrow{A}.\overrightarrow{B}=0$

Hence the two vectors are perpendicular to each other.