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KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    On which of the following lines lies the point of intersection of the line, \[\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}\] and the plane, \[x+y+z=2?\]

    A) \[\frac{x+3}{3}=\frac{4-y}{3}=\frac{z+1}{-2}\]           

    B) \[\frac{x-4}{1}=\frac{y-5}{1}=\frac{z-5}{-1}\]

    C) \[\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+4}{-5}\]

    D) \[\frac{x-2}{2}=\frac{y-3}{2}=\frac{z+3}{3}\]

    Correct Answer: C

    Solution :

    Put\[(2\lambda +4,2\lambda +5,\lambda +3)\]in\[x+y+z=2\]
    \[2\lambda +4+2\lambda +5+\lambda +3=2\]
    \[5\lambda =-10\]           \[\lambda =-2\]
    \[P(0,1,1)\]
    Now put in options
    Answer is C.


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