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Dear Student

Here, If condition is
$$\begin{gathered} \left|\overrightarrow{A}+\overrightarrow{B}\right| =\left|\overrightarrow{A}-\overrightarrow{B}\right| \\ That is magnitude is equal then \\ \sqrt{A^2+B^2+2AB Cos\theta } = \sqrt{A^2+B^2-2AB Cos\theta } \\ Squaring both sides \\ {A}^2+B^2+2AB Cos\theta =A^2+B^2-2AB Cos\theta \\ 4AB Cos\theta =0 \\ So \\ \theta ={90}^o \\ Hence \\ \overrightarrow{A}.\overrightarrow{B} =0 \end{gathered}$$
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