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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 \[\theta \] be the angle between the vectors \[12+m-2=0\] and \[\mathbf{b}=6\mathbf{i}-3\mathbf{j}+2\mathbf{k}\], then [MP PET 2001, 03]

    A)             \[\cos \theta =\frac{4}{21}\]

    B)             \[\cos \theta =\frac{3}{19}\]

    C)             \[\cos \theta =\frac{2}{19}\]

    D)             \[\cos \theta =\frac{5}{21}\]

    Correct Answer: A

    Solution :

                    \[\cos \theta =\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{a}|\,\,\,|\mathbf{b}|}=\frac{12-6-2}{\sqrt{4+4+1}\sqrt{36+9+4}}=\frac{4}{21}\].


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