If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is

 Magnitude of sum of two vectors   $=|\overrightarrow{A}+\overrightarrow{B}|$

Magnitude of difference of two vectors   $=|\overrightarrow{A}-\overrightarrow{B}|$

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

$\Rightarrow {(A^2+B^2+2AB\cos \theta )}^{1/2}={(A^2+B^2-2AB\cos \theta )}^{1/2}$

$\Rightarrow A^2+B^2+2AB\cos \theta =A^2+B^2-2AB\cos \theta$

$\begin{array}{rl} & \Rightarrow 4AB\cos \theta =0\\ & \Rightarrow \cos \theta =0\\ & \Rightarrow \theta ={90}^{\circ }\end{array}$