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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If \[|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}|\,\,=4\] and \[|\mathbf{a}+\mathbf{b}|\,\,=5,\] then \[|\mathbf{a}-\mathbf{b}|\,\,=\]                                           [EAMCET 1994]

    A) 6             

    B) 5

    C) 4             

    D) 3

    Correct Answer: B

    Solution :

    We have \[|\mathbf{a}+\mathbf{b}{{|}^{2}}+|\mathbf{a}-\mathbf{b}{{|}^{2}}=2(|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}})\] \[\therefore \,\,\,25+|\mathbf{a}-\mathbf{b}{{|}^{2}}=2(9+16)\Rightarrow |\mathbf{a}-\mathbf{b}|=5\].


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