If $\left|\overrightarrow{A}+\overrightarrow{B}\right|=\left|\overrightarrow{A}-\overrightarrow{B}\right|$ ,then the magnitude of $\overrightarrow{B}$  is

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

${\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}+2\text{AB}\cos \theta ={\text{A}}^{\text{2}}+{\text{B}}^{\text{2}}-2\text{AB}\cos \theta$

$4\text{AB}\cos \theta =0$

$\Rightarrow \cos \theta =0\Rightarrow \theta =\frac{\pi }{2}$

If $\left|\overrightarrow{B}\right|$ zero also above condition is satisfied