Answer:
Given, \[|\vec{A}+\,\vec{B}|=|\vec{A}-\,\vec{B}|\]or\[{{\text{A}}^{\text{2}}}+{{\text{B}}^{\text{2}}}+\text{2AB}\,\text{cos}\theta
={{\text{A}}^{\text{2}}}+{{\text{B}}^{\text{2}}}\text{2ABcos}\theta \]. or \[\text{4
AB cos}\theta =0\]or\[\text{cos}\theta =0\]or\[\theta =\text{ 9}0{}^\circ \]. i.e.
the two vectors are perpendicular to each other.
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