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

  • question_answer
    Let \[\mathbf{b}=3\mathbf{j}+4\mathbf{k},\,\,\mathbf{a}=\mathbf{i}+\mathbf{j}\] and let \[{{\mathbf{b}}_{1}}\] and \[{{\mathbf{b}}_{2}}\] be component vectors of b parallel and perpendicular to a. If \[{{\mathbf{b}}_{1}}=\frac{3}{2}\mathbf{i}+\frac{3}{2}\mathbf{j}\], then \[{{\mathbf{b}}_{2}}=\] [MP PET 1989]

    A)             \[\frac{3}{2}\mathbf{i}+\frac{3}{2}\mathbf{j}+4\mathbf{k}\]

    B)             \[-\frac{3}{2}\mathbf{i}+\frac{3}{2}\mathbf{j}+4\mathbf{k}\]

    C)             \[-\frac{3}{2}\mathbf{i}+\frac{3}{2}\mathbf{j}\]

    D)             None of these

    Correct Answer: B

    Solution :

                    \[{{\mathbf{b}}_{2}}=\mathbf{b}-{{\mathbf{b}}_{1}}=-\frac{3}{2}\mathbf{i}+\frac{3}{2}\mathbf{j}+4\mathbf{k}\] and obviously \[{{\mathbf{b}}_{2}}\] is perpendicular to\[\mathbf{a}.\]


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