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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 vector \[\mathbf{a}=2\mathbf{i}-3\mathbf{j}+6\mathbf{k}\] and vector \[\mathbf{b}=-2\mathbf{i}+2\mathbf{j}-\mathbf{k},\] then \[\frac{\text{Projection of vector }\mathbf{a}\text{ on vector }\mathbf{b}}{\text{Projection of vector }\mathbf{b}\text{ on vector }\mathbf{a}}=\]        [MP PET 1994, 99; Pb. CET 2000]

    A)             \[\frac{3}{7}\]

    B)             \[\frac{7}{3}\]

    C)             3

    D)             7

    Correct Answer: B

    Solution :

                    Required value \[={\frac{\mathbf{b}\,.\,\mathbf{a}}{|\mathbf{b}|}}/{\frac{\mathbf{a}\,.\mathbf{b}}{|\mathbf{a}|}}\;=\frac{|\mathbf{a}|}{|\mathbf{b}|}=\frac{7}{3}.\]


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