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

  • question_answer
    The value of k for which the vectors \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=-2\,\mathbf{i}+k\,\mathbf{j}\] are collinear is                                 [Pb. CET 2004]

    A) 2

    B) \[\frac{1}{2}\]

    C)             \[\frac{1}{3}\]       

    D) 3

    Correct Answer: A

    Solution :

    Since \[\mathbf{a}\]and \[\mathbf{b}\]are collinear, we have \[\mathbf{a}=m\mathbf{b}\]for some scalar m. Þ  \[\mathbf{i}-\mathbf{j}=m\text{ }(-2\mathbf{i}+k\mathbf{j})\]Þ \[\mathbf{i}-\mathbf{j}=-2m\mathbf{i}+km\mathbf{j}\] Þ  \[-2m=1,\,km=-1\] \  \[m=-\frac{1}{2},\] So \[k=2\].            


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