Two vectors ( A ) and ( B ) are such that (| A + B |=| A - B | )....

($\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=| \overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}} \mid$) (\Rightarrow $\sqrt{\mathrm{A}^2+\mathrm{B}^2+2 \mathrm{AB} \cos \theta}=\sqrt{\mathrm{A}^2+\mathrm{B}^2-2 \mathrm{AB} \cos \theta}$) Squaring both the sides, we get (\overrightarrow{\mathrm{A}}^2+\overrightarrow{\mathrm{B}}^2+2 \overrightarrow{\mathrm{A}} \overrightarrow{\mathrm{B}} \cos \theta=\overrightarrow{\mathrm{A}}^2+\overrightarrow{\mathrm{B}}^2-2 $\overrightarrow{\mathrm{A}} \overrightarrow{\mathrm{B}} \cos \theta$) or (4 $\overrightarrow{\mathrm{A}} \overrightarrow{\mathrm{B}} \cos \theta=$0) or (\cos $\theta=$0) (since the scalar or dot product is zero). Therefore angle between ($\overrightarrow{\mathrm{A}}$) to ($\overrightarrow{\mathrm{B}}$) is (90^{{}^{\circ}})