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

  • question_answer
    If the vectors \[3i+\lambda \,j+k\] and \[2i-j+8k\] are perpendicular, then \[\lambda \] is [Kerala (Engg.) 2002]

    A)             ? 14

    B)             7

    C)             14

    D)             1/7      

    Correct Answer: C

    Solution :

               Let \[\mathbf{a}=3\mathbf{i}+\lambda \,\mathbf{j}+\mathbf{k}\],\[\mathbf{b}=2\mathbf{i}-\mathbf{j}+8\mathbf{k}\]                    \[\because \,\,\mathbf{a}\bot \,\mathbf{b}\], \ \[\mathbf{a}\,\mathbf{.}\,\mathbf{b}=0\]                    \[(3\mathbf{i}+\lambda \,\mathbf{j}+\mathbf{k})\,\mathbf{.}\,(2\mathbf{i}-\mathbf{j}+8\mathbf{k})=0\]                 \[\mathbf{a},\,\mathbf{b},\,\mathbf{c}\] \[\Rightarrow \lambda =14.\]


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