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MHT CET2019Morning ShiftMathematicsThree Dimensional GeometryActual

The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes x + 2 y + 3 z = 4 and 4 x + 3 y + 2 z = 1 are …

Options

  1. A2,3 , 1
  2. B1,2 , 3
  3. C3,1 , 2
  4. D3,2 , 1

Correct answer

D. 3,2 , 1

Step-by-step solution

We have, line of intersection of the planes x + 2 y + 3 z = 4 and 4 x + 3 y + 2 z = 1 ∴ Equation of plane passing through the given planes is x + 2 y + 3 z - 4 + λ 4 x + 3 y + 2 z - 1 = 0 ⇒ 1 + 4 λ x + 2 + 3 λ y + 3 + 2 λ + - 4 - λ = 0 Since, plane passing through origin ∴ - 4 - λ = 0 ⇒ λ = - 4 Now, equation of plane is 1 - 16 x + 2 - 12 y + 3 - 8 z + 0 = 0 ⇒ - 15 x - 10 y - 5 z = 0 ⇒ 3 x + 2 y + z = 0 ∴ Direction rations of the normal to the plane are 3, 2, 1.

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