Answer:
As the vectors \[\vec{A}+\vec{B}\] and \[\vec{A}-\vec{B}\] are perpendicular to each other, therefore \[(\vec{A}+\vec{B}).(\vec{A}-\vec{B})=0\] \[\vec{A}.\vec{A}-\vec{A}.\vec{B}+\vec{B}.\vec{A}-\vec{B}.\vec{B}=0\] or \[{{A}^{2}}-{{B}^{2}}=0\] \[\Rightarrow \] \[A=B\] \[[\because \vec{A}.\vec{B}=\vec{B}.\vec{A}]\]
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