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JEE Main20199 Jan 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The plane through the intersection of the planes x + y + z = 1 and 2 x + 3 y - z + 4 = 0 and parallel to y - axis also passes through the point

Options

  1. A3 , 3 , - 1
  2. B- 3 , 1 , 1
  3. C3 , 2 , 1
  4. D- 3 , 0 , - 1

Correct answer

C. 3 , 2 , 1

Step-by-step solution

Let required plane is (using concept of family of plane) x + y + z - 1 + t 2 x + 3 y - z + 4 = 0 ⇒ 1 + 2 t x + 1 + 3 t y + 1 - t z - 1 + 4 t = 0 Again D R of y - axis is 0 , 1 , 0 Since plane is parallel to y - axis Hence 1 + 2 t × 0 + 1 + 3 t × 1 + 1 - t × 0 = 0 ⇒ t = - 1 3 ∴ required plane is 1 3 x + 4 3 z - 7 3 = 0 ⇒ x + 4 z - 7 = 0 Which satisfy 3 , 2 , 1

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