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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2010

  • question_answer
    The distance from the point (3,4,5) to the point where the line\[\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\] meets the plane\[x+y+z=17\]is

    A)  1                

    B)  2

    C)  3                

    D)  4

    Correct Answer: C

    Solution :

     Consider a point\[(r+3,\text{ }2r+4,\text{ }2r+5)\]on the given line. This point lies on the plane\[x+y+z=17,\]then \[r+3+2r+4+2r+5=17\] \[\Rightarrow \] \[5r=17-12=5\Rightarrow r=1\] Thus, intersection point of the line and the plane is (4, 6, 7). Now, distance between the points (3, 4, 5) and (4, 6, 7) is \[\sqrt{1+4+4}=3\]


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