Answer:
\[(\vec{A}+\vec{B})=(\vec{A}-\vec{B})\] \[\therefore \] \[{{(\vec{A}+\vec{B})}^{2}}={{(\vec{A}-\vec{B})}^{2}}\] or \[{{A}^{2}}+{{B}^{2}}+2\vec{A}.\vec{B}={{A}^{2}}+{{B}^{2}}-2\vec{A}.\vec{B}\] or \[4\vec{A}.\vec{B}=0\] or \[\vec{A}.\vec{B}=0\] This implies that \[\vec{A}\] and \[\vec{B}\] are perpendicular to each other.
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