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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A plane P = 0 , which is perpendicular to line x - 2 2 = y + 2 2 = z - 1 1 is passing through the point at which the above line meets the plane x + y + z = 21 , then the distance of plane P = 0   from origin is

Options

  1. A7 3
  2. B5
  3. C32 3
  4. D37 3

Correct answer

D. 37 3

Step-by-step solution

Any general point on the line is 2 λ + 2,   2 λ - 2 ,   λ + 1 This point most satisfy x + y + z = 21 Hence 2 λ + 2 + 2 λ - 2 + λ + 1 = 21 ⇒ λ = 4 So, the point of intersection of line and plane is ( 10 ,   6 ,   5 ) So, equation of plane P = 0 is 2 x - 10 + 2 ( y - 6 ) + 1 ( z - 5 ) = 0 ⇒ 2 x + 2 y + z - 37 = 0 Hence, distance of P = 0 from origin is = 37 3 = 37 3

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