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

  • question_answer
    The value of x for which the angle between the vectors \[\mathbf{a}=x\mathbf{i}-3\mathbf{j}-\mathbf{k},\,\,\mathbf{b}=2x\mathbf{i}+x\mathbf{j}-\mathbf{k}\] is acute and the angle between the vectors b and the axis of ordinate is obtuse, are

    A)             1, 2

    B)             ? 2, ? 3

    C)             x > 0

    D)             None of these

    Correct Answer: B

    Solution :

               According to the given conditions, \[\mathbf{a}\,.\,\mathbf{b}>0\] and \[\mathbf{b}\,.\,\mathbf{c}<0,\] where \[\mathbf{c}=(0,\,\,1,\,\,0).\]                                 \[\Rightarrow 2{{x}^{2}}-3x+1>0\] and \[x<0.\] Hence the result.


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