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JEE Main202324 Jan 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point - 1 , 9 , - 16 from the plane 2 x + 3 y - z = 5 measure parallel to the line x + 4 3 = 2 - y 4 = z - 3 12 is

Options

  1. A13 2
  2. B31
  3. C26
  4. D20 3

Correct answer

C. 26

Step-by-step solution

Equation of line passing through - 1 , 9 , - 16 and parallel to x + 4 3 = y - 2 - 4 = z - 3 12 is x + 1 3 = y - 9 - 4 = z + 16 12 = λ Any point on this line is P 3 λ - 1 ,   - 4 λ + 9 ,   12 λ - 16 For finding point of intersection of line and a plane, we have 6 λ - 2 - 12 λ + 27 - 12 λ + 16 = 5 ⇒ λ = 2 So, P 5 , 1 , 8 Required distance is = 5 + 1 2 + 1 - 9 2 + 8 + 16 2 =   36 + 64 + 576 = 26 units

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