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JEE Main202324 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let the plane containing the line of intersection of the planes P 1 : x + λ + 4 y + z = 1 and P 2 : 2 x + y + z = 2 pass through the points 0 , 1 , 0 and 1 , 0 , 1 . Then the distance of the point 2 λ , λ , - λ from the plane P 2 is

Options

  1. A5 6
  2. B4 6
  3. C2 6
  4. D3 6

Correct answer

D. 3 6

Step-by-step solution

Given, Equation of planes P 1 :   x + λ + 4 y + z = 1 and P 2 :   2 x + y + z = 2 Now we know that equation of plane passing through the planes P 1   &   P 2 is given by P 1 + k P 2 = 0 Now given it is passing through the points 0 , 1 , 0 and 1 , 0 , 1 , So, x + λ + 4 y + z - 1 + k 12 x + y + z - 2 = 0 when passing through 0 , 1 , 0 we get, 0 + λ + 4 1 + 0 - 1 + k 12 × 0 + 1 + 0 - 2 = 0 ⇒ λ + 4 - 1 - k = 0 ⇒ λ + 3 - k = 0   . . . . . . . . 1 And

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