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MHT CET20228 Aug 2022Evening ShiftMathematicsThree Dimensional GeometryActual

Then foot of the perpendicular from the point (0,2,3) on the line x+3 5 = y-1 2 = z+4 3

Options

  1. A(2,3,1)
  2. B(2,3,-1)
  3. C(2,-3,1)
  4. D(-2,3,1)

Correct answer

B. (2,3,-1)

Step-by-step solution

Any point on the line x+3 5 = y-1 3 = z+4 3 = can be taken as (5 -3,2 +1,3 -4) for foot of perpendicular = a ( -x₁ )+b ( -y₁ )+c ( -z₁ ) a^2+b^2+c^2 aligned & = 5(0+3)+2(2-1)+3(3+4) 5^2+2^2+3^2 & = 38 38 =1 aligned Hence foot of perpendicular is (5 1-3,2 1+1,3 1-4) (2,3,-1)

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