If the image of the point P(1,−2,3) in the plane, 2x+3y−4z+22=0 measured parallel to the line, x1=y4=z5 is Q, then PQ is equal to

If the image of the point P(1,2,3) in the plane, 2x+3y4z+22=0 measured parallel to the line, x1=y4=z5 is Q, then PQ is equal to

  1. A

    242

  2. B

    42

  3. C

    65

  4. D

    35

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    Solution:

    Equation of the line passing through P(1,2,3)

    with dr's (1,4,5) is x11=y+24=z35=t

    R(t+1,4t2,5t+3) lies on the plane then t = 1    ,R (2,2,8)

    PQ=2PR=21+16+25=242

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