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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 \[a=2i+j+2k\] and \[b=5i-3j+k,\] then the projection of b on a is [Karnataka CET 2002]

    A)             3

    B)             4

    C)             5

    D)             6

    Correct Answer: A

    Solution :

               Vectors \[a=2i+j+2k\] and \[\mathbf{b}=5i-3j+k\]. We know that the projection of b on                                     \[a=\frac{b\,.\,a}{|\mathbf{a}|}=\frac{(2i+j+2k)\,.\,(5i-3j+k)}{\sqrt{{{(2)}^{2}}+{{(1)}^{2}}+{{(2)}^{2}}}}=\frac{10-3+2}{\sqrt{9}}=\frac{9}{3}=3.\]


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