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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:
Explanation
$|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$ Squaring on both sides $|\vec{A} + \vec{B}|^{2} = |\vec{A} - \vec{B}|^{2}$ $\Rightarrow \vec{A} \cdot \vec{A} + 2\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{B} = \vec{A} \cdot \vec{A} - 2\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{B}$ $\Rightarrow 4\vec{A} \cdot \vec{B} = 0 \Rightarrow 4AB \cos \theta = 0 \Rightarrow \cos \theta = 0 \Rightarrow \theta = 90^{\circ}$