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JEE Main202127 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The distance of the point 1 , - 2 , 3 from the plane x - y + z = 5 measured parallel to a line, whose direction ratios are 2 , 3 , - 6 , is

Options

  1. A2
  2. B5
  3. C3
  4. D1

Correct answer

D. 1

Step-by-step solution

Given, equation of plane x - y + z = 5 , Point is 1 , - 2 , 3 And the direction ratio of plane parallel to the given plane is 2 , 3 , - 6 Therefore, Equation of plane when D.R of parallel plane is given is, x - 1 2 = y + 2 3 = z - 3 - 6 = λ ⇒ x = 2 λ + 1   ,   y = 3 λ - 2     ,   z = - 6 λ + 3 since, x - y + z = 5 ⇒ 2 λ + 1 - 3 λ + 2 - 6 λ + 3 = 5 ⇒ λ = 1 7 ⇒ x = 9 7   ,   y = - 11 7   ,   z = 15 7 Distance

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