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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Introduction to Three Dimensional Geometry

  • question_answer
    If x co-ordinates of a point P of line joining the points Q (2, 2, 1) and R (5, 2, - 2) is 4, then the z-coordinates of P is

    A) -2

    B) -1   

    C) 1

    D) 2

    Correct Answer: B

    Solution :

    [b] Suppose P divides QR in ration \[:1\]. Then, co-ordinates of P are \[\left( \frac{5\lambda +2}{\lambda +1},\frac{\lambda +2}{\lambda +1},\frac{-2\lambda +1}{\lambda +1} \right)\]. It is given that the x-coordinate of P is 4. i.e., \[\frac{5\lambda +2}{\lambda +1}=4\Rightarrow \lambda =2\] So, z-coordinate of P is \[\frac{-2\lambda +1}{\lambda +1}=\frac{-4+1}{2+1}=-1.\]


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