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If $\vec{A}$ and $\vec{B}$ are non-zero vectors which obey the relation $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$, then the angle between them is
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The correct answer is:
$90^{\circ}$
$\begin{aligned} \text { } & |\vec{A}+\vec{B}|=|\vec{A}-\vec{B}| \\ & |\vec{A}|^2+|\vec{B}|^2+2|\vec{A}||\vec{B}| \cos \theta \\ & =|\vec{A}|^2+|\vec{B}|^2-2|\vec{A}||\vec{B}| \cos \theta \\ \therefore & \cos \theta=0 \Rightarrow \theta=90^{\circ}\end{aligned}$
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