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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    If the position vectors of A, B, C, D are \[2\,\mathbf{i}+\mathbf{j},\] \[\mathbf{i}-3\,\mathbf{j},\] \[3\,\mathbf{i}+2\,\mathbf{j}\] and \[\mathbf{i}+\lambda \mathbf{j}\] respectively and \[\overrightarrow{AB}||\overrightarrow{CD}\] , then \[\lambda \] will be                                                                                                                           [RPET 1988]

    A) 8             

    B) 6

    C) 8             

    D) 6

    Correct Answer: B

    Solution :

    \[\overrightarrow{AB}=-\mathbf{i}-4\mathbf{j},\] \[\overrightarrow{CD}=-2\mathbf{i}+(\lambda -2)\mathbf{j}\] \[\because \,\overrightarrow{AB}\,||\overrightarrow{CD}\].  So ,\[\frac{-1}{-2}=\frac{-4}{\lambda -2}\], \[\lambda -2=-8\] or \[\lambda =-6.\]


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