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JEE Main20231 Feb 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let the image of the point P 2 , - 1 , 3 in the plane x + 2 y - z = 0 be Q . Then the distance of the plane 3 x + 2 y + z + 29 = 0 from the point Q is

Options

  1. A22 2 7
  2. B24 2 7
  3. C2 14
  4. D3 14

Correct answer

D. 3 14

Step-by-step solution

We have, Equation of line P M is x - 2 1 = y + 1 2 = z - 3 - 1 = λ Any point on the line is M ≡ λ + 2 , 2 λ - 1 , - λ + 3 Point M lies on the plane, so λ + 2 + 2 2 λ - 1 - 3 - λ = 0 ⇒ λ = 1 2 Point M ≡ 5 2 , 0 , 5 2 For Image Q α , β , γ , we have α + 2 2 = 5 2 , β - 1 2 = 0 γ + 3 2 = 5 2 So, Q ≡ 3 , 1 , 2 Distance of the point Q from the plane 3 x + 3 y + z + 29 = 0 is d = 3 3 + 2 1 + 2 + 29 3 2 + 2 2 + 1 2 ⇒ d = 42

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