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

  • question_answer
    \[(\mathbf{a}\,.\,\mathbf{i})\,\mathbf{i}+(\mathbf{a}\,.\,\mathbf{j})\mathbf{j}+(\mathbf{a}\,.\,\mathbf{k})\,\mathbf{k}=\]                                                            [Karnataka CET 2004]

    A)             a

    B)             2 a

    C)             0

    D)             None of these

    Correct Answer: A

    Solution :

                    Let \[\mathbf{a}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\]. Then  \[(\mathbf{a}.\mathbf{i})\mathbf{i}+(\mathbf{a}.\mathbf{j})\mathbf{j}+(\mathbf{a}.\mathbf{k})\mathbf{k}=\mathbf{a}.\]


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