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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-6

  • question_answer
    The ratio in which the line joining \[\left( \mathbf{1},\mathbf{2},\mathbf{3} \right)\] and \[\left( -\mathbf{3},\mathbf{4},-\mathbf{5} \right)\] is divided by \[\mathbf{xy}\]plane is:

    A)  \[5:3\]              

    B) \[2:3\]        

    C)  \[3:2\]              

    D)  \[3:5\]

    Correct Answer: D

    Solution :

    [d] Let the ratio be \[\lambda :1\] Dividing point \[P\equiv \left( \frac{-3\lambda +1}{\lambda +1},\frac{4\lambda +2}{\lambda +1},\frac{-5\lambda +1}{\lambda +1} \right)\] Since, this point lies in xy plane. \[\therefore \] z-coordinate will be zero. i.e. \[\frac{-5\lambda +3}{\lambda +1}=\frac{0}{1}\] \[\therefore -5A+3=0\] \[\therefore \lambda =\frac{3}{5}\] Hence, option [d] is correct.


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