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

  • question_answer
    If \[\mathbf{a}=2\mathbf{i}+\mathbf{j}-8\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}+3\mathbf{j}-4\mathbf{k},\] then the magnitude of \[\mathbf{a}+\mathbf{b}=\]                                              [MP PET 1996]

    A) 13          

    B) \[\frac{13}{3}\]

    C) \[\frac{3}{13}\]    

    D) \[\frac{4}{13}\]

    Correct Answer: A

    Solution :

    \[|\mathbf{a}+\mathbf{b}|\,=\,|3\mathbf{i}+4\mathbf{j}-12\mathbf{k}|\,=\,|\sqrt{{{3}^{2}}+{{4}^{2}}+{{12}^{2}}}|\,=13\]                 \[\therefore \,\,\,\mathbf{a}+\mathbf{b}=13\].


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