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

  • question_answer
    If \[\mathbf{a}=2\,\mathbf{i}+2\,\mathbf{j}+3\,\mathbf{k},\,\,\mathbf{b}=-\mathbf{i}+2\,\mathbf{j}+\mathbf{k}\] and \[c=3\,\mathbf{i}+\mathbf{j},\] then \[\mathbf{a}+t\,\mathbf{b}\] is perpendicular to c if \[t=\] [MNR 1979; MP PET 2002]

    A)             2

    B)             4

    C)             6

    D)             8

    Correct Answer: D

    Solution :

               \[\mathbf{a}+t\mathbf{b}=2\mathbf{i}+2\mathbf{j}+3\mathbf{k}+(-t\mathbf{i}+2t\mathbf{j}+t\mathbf{k})\]                             \[=(2-t)\mathbf{i}+(2+2t)\mathbf{j}+(3+t)\mathbf{k}\]                    Given that it is perpendicular to \[\mathbf{c}=3\mathbf{i}+\mathbf{j}\]                    Hence \[(2-t)3+(2+2t)1+(3+t)0=0\]                                 \[\Rightarrow 6-3t+2+2t=0\Rightarrow t=8.\]


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