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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}\] and \[\mathbf{b}=3\mathbf{i}+6\mathbf{j}+2\mathbf{k},\] then a vector in the direction of a and having magnitude as |b| is     [IIT 1983]

    A) \[7\,(\mathbf{i}+\mathbf{j}+\mathbf{k})\]         

    B) \[\frac{7}{3}\,(\mathbf{i}+2\mathbf{j}+2\mathbf{k})\]

    C)             \[\frac{7}{9}\,(\mathbf{i}+2\mathbf{j}+2\,\mathbf{k})\]   

    D) None of these

    Correct Answer: B

    Solution :

    \[|\mathbf{b}|\mathbf{\hat{a}}=\sqrt{9+36+4}\left( \frac{\mathbf{i}+2\mathbf{j}+2\mathbf{k}}{\sqrt{1+4+4}} \right)=\frac{7}{3}(\mathbf{i}+2\mathbf{j}+2\mathbf{k}).\]


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