question_answer

Under what condition does the equality: \[|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|\] hold good?

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.