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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The sum of the intercepts of the plane on the coordinate axes, passing through the intersection of the planes 2 x + 3 y + 3 z - 5 = 0 and 2 x - 5 y + 3 z + 1 = 0 and parallel to the line x - 1 2 = y - 2 - 5 = z - 3 - 7 , is

Options

  1. A2 5
  2. B11 105
  3. C11 102
  4. D3 101

Correct answer

C. 11 102

Step-by-step solution

Equation of the plane passing through the line of intersection of the 2 given planes is 2 x + 3 y + 3 z - 5 + λ 2 x - 5 y + 3 z + 1 = 0 ⇒ x 2 + 2 λ + y 3 - 5 λ + z 3 + 3 λ + λ - 5 = 0 ∵ This plane is parallel to x - 1 2 = y - 2 - 5 = z - 3 - 7 ⇒ 2 2 + 2 λ - 5 3 - 5 λ - 7 3 + 3 λ = 0 ⇒ 4 + 4 λ - 15 + 25 λ - 21 - 21 λ = 0 ⇒ 8 λ - 32 = 0 ⇒ λ = 4 So, equation of the plane is 10 x - 17 y + 15 z - 1 = 0 Sum of intercepts = 1 10 - 1 17 + 1 15 = 51 - 30 + 34 510 = 55 510 = 11 102

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