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JEE Main & Advanced Physics Vectors Question Bank Addition and Subtraction of Vectors

  • question_answer
    The vector sum of two forces is perpendicular to their vector differences. In that case, the forces               [CBSE PMT 2003]

    A)                 Are equal to each other in magnitude

    B)                 Are not equal to each other in magnitude

    C)                 Cannot be predicted     

    D)                 Are equal to each other

    Correct Answer: A

    Solution :

                        If two vectors are perpendicular then their dot product must be equal to zero. According to problem                                 \[(\overrightarrow{A}+\overrightarrow{B}).(\overrightarrow{A}-\overrightarrow{B})=0\]Þ\[\overrightarrow{A}.\overrightarrow{A}-\overrightarrow{A}.\overrightarrow{B}+\overrightarrow{B}.\overrightarrow{A}-\overrightarrow{B}.\overrightarrow{B}=0\]                                 Þ\[{{A}^{2}}-{{B}^{2}}=0\]Þ\[{{A}^{2}}={{B}^{2}}\]                                 \[\therefore \] \[A=B\] i.e. two vectors are equal to each other in magnitude.


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