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JEE Main & Advanced Mathematics Vector Algebra Question Bank Scaler or Dot product of two vectors and its application

  • question_answer
    If \[|a|\,=\,|\mathbf{b}|,\] then \[(a+b)\,.\,(a-b)\] is             [MP PET 2002]

    A)             Positive

    B)             Negative

    C)             Zero

    D)             None of these

    Correct Answer: C

    Solution :

               \[(a+b)\,.\,(a-b)=a.a+b.a-b.a-b.b\]                             \[=a.a-b.b=\,|a{{|}^{2}}-|b{{|}^{2}}\]                                       \[=0\],       \[(\because \,|\mathbf{a}|\,=\,|\mathbf{b}|)\].


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