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

  • question_answer
    The angle between the vectors \[(2\mathbf{i}+6\mathbf{j}+3\mathbf{k})\] and \[(12\mathbf{i}-4\mathbf{j}+3\mathbf{k})\] is                                   [MP PET 1996]

    A)             \[{{\cos }^{-1}}\left( \frac{1}{10} \right)\]

    B)             \[{{\cos }^{-1}}\left( \frac{9}{11} \right)\]

    C)             \[{{\cos }^{-1}}\left( \frac{9}{91} \right)\]

    D)             \[{{\cos }^{-1}}\left( \frac{1}{9} \right)\]

    Correct Answer: C

    Solution :

               \[\theta ={{\cos }^{-1}}\left( \frac{2\times 12+6\times (-4)+3(3)}{\sqrt{{{2}^{2}}+{{6}^{2}}+{{3}^{2}}}\sqrt{{{12}^{2}}+{{4}^{2}}+{{3}^{2}}}} \right)\]                   \[={{\cos }^{-1}}\left( \frac{9}{7\times 13} \right)={{\cos }^{-1}}\left( \frac{9}{91} \right)\]


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