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JEE Main201910 Apr 2019Evening ShiftMathematicsThree Dimensional GeometryActual

If the plane 2 x - y + 2 z + 3 = 0 has the distances 1 3 and 2 3 units from the planes 4 x - 2 y + 4 z + λ = 0 and 2 x - y + 2 z + μ = 0 , respectively, then the maximum value of λ + μ is equal to:

Options

  1. A9
  2. B15
  3. C13
  4. D5

Correct answer

C. 13

Step-by-step solution

The distance between the parallel planes a x + b y + c z + d 1 = 0 and a x + b y + c z + d 2 = 0 is d 1 - d 2 a 2 + b 2 + c 2 . Given, the distance between the planes 2 x - y + 2 z + 3 = 0 and 4 x - 2 y + 4 z + λ = 0 ,     ⇒ 2 x - y + 2 z + λ 2 = 0 is 1 3 units ⇒ λ 2 - 3 4 + 1 + 4 = 1 3 ⇒ λ 2 - 3 3 = 1 3 ⇒ λ 2 - 3 = 1 ⇒ λ 2 - 3 = 1 or λ 2 - 3 = - 1 ⇒ λ = 8 or λ = 4 . Also, distance between the planes 2 x - y + 2 z + 3 = 0 and

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