MathematicsPerpendiculars are drawn from points on the line x+22=y+1−1=z3 to the plane x+y+z=3. The feet of perpendiculars lie on the line

Perpendiculars are drawn from points on the line x+22=y+11=z3 to the plane x+y+z=3. The feet of perpendiculars lie on the line

  1. A

    x5=y18=z213

  2. B

    x2=y13=z25

  3. C

    x4=y13=z27

  4. D

    x2=y17=z25

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    Solution:

    Let x+22=y+11=z3=k then (2k2, k1, 3k) is a
    point on the line. Let the foot of the perpendicular from this point on the plane x + y + z 3 = 0 be

    (α,β,γ) then it is given by

    α(2k2)1=β(k1)1=γ3k1

    =(2k2)+(k1)+(3k)33=64k3

    Thus, α=2k3,β=17k3,γ=2+5k3 then the line is
    given by x2/3=y17/3=z25/3

     i.e., x2=y17=z25

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