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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 \[\mathbf{a}=-\,3\mathbf{i}+x\mathbf{j}+\mathbf{k}\] and \[\mathbf{b}=x\mathbf{i}+2x\mathbf{j}+\mathbf{k}\] is acute and the angle between b and x-axis lies between \[\pi /2\] and \[\pi \]satisfy                                     [Kurukshetra CEE 1996]

    A)             \[x>0\]

    B)             \[x<0\]

    C)             \[x>1\] only

    D)             \[x<-1\] only

    Correct Answer: B

    Solution :

               For acute angle \[\mathbf{a}\,.\,\mathbf{b}>0\]            i.e., \[-3x+2{{x}^{2}}+1>0\Rightarrow (x-1)(2x-1)>0\]            For obtuse angle between \[\mathbf{b}\] and x-axis \[\mathbf{b}\,.\,\mathbf{i}<0\]                 Þ \[x<0\].


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