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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    The equation of the plane passing through the mid-point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it, is

    A)  \[x+y+z=9\]

    B)  \[x+y+z=-9\]

    C)  \[2x+3y+4z=9\]

    D)  \[2x+3y+4z=-9\]

    Correct Answer: A

    Solution :

    The DR's of the joining of the points (1, 2, 3) and (3, 4, 5) are (3-1,4-2,5-3), i.e., (2, 2, 2). Also, the mid-point of the join of the points (1, 2, 3) and (3, 4, 5) is (2, 3, 4). \[\therefore \]Equation of plane which passes through (2, 3, 4) and the DR's of its normal are (2, 2, 2) is \[2(x-2)+2(y-3)+2(z-4)=0\] \[\Rightarrow \]         \[~x+y+z-9=0\] \[\Rightarrow \] \[x+y+z=9\]


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