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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

  • question_answer
    The condition for \[\overrightarrow{A}+\overrightarrow{B}\] to be perpendicular to \[\overrightarrow{A}-\overrightarrow{B}\] is that

    A) \[|\overrightarrow{A}|\,\,=\,\,|\overrightarrow{B}|\]        

    B)        \[\overrightarrow{\text{A}}\,\,\text{=}\,\,\overrightarrow{\text{B}}\]

    C) \[\overrightarrow{\text{B}}\text{ =}\,\,\text{0 }\!\!~\!\!\text{ }\]   

    D)        \[\text{ }\!\!|\!\!\text{ }\,\overrightarrow{\text{A}}\,\text{+}\,\overrightarrow{\text{B}}\,\text{ }\!\!|\!\!\text{ }\,\,\text{= }\!\!|\!\!\text{ }\,\overrightarrow{\text{A}}-\overrightarrow{\text{B}}\,\,\text{ }\!\!|\!\!\text{ }\]

    Correct Answer: A

    Solution :

    [a] \[\text{(\vec{A}+\vec{B})}\text{.(\vec{A}}-\text{\vec{B})}=0\] or \[\text{\vec{A}}\,\text{.}\,\text{\vec{A}+\vec{B}}\,\text{.}\,\text{\vec{A}}-\text{\vec{A}}\,\text{.}\,\text{\vec{B}}-\text{\vec{B}}\,\text{.}\,\text{\vec{B}}=0\] \[\therefore \,\,\,\text{A=B}\text{.}\]


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