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JEE Main20199 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane containing the straight line x 2 = y 3 = z 4 and perpendicular to the plane containing the straight lines x 3 = y 4 = z 2 and x 4 = y 2 = z 3 is:

Options

  1. A3 x + 2 y - 3 z = 0
  2. Bx + 2 y - 2 z = 0
  3. Cx - 2 y + z = 0
  4. D5 x + 2 y - 4 z = 0

Correct answer

C. x - 2 y + z = 0

Step-by-step solution

Direction Ratio of 2 nd given plane is i ^ j ^ k ^ 3 4 2 4 2 3 = 8 i ^ - j ^ - 10 k ^ ∴ Direction Ratio of 2 nd given plane = 8 , - 1 , - 10 ∴ Direction Ratio of required plane is i ^ j ^ k ^ 8 - 1 - 10 2 3 4 = 26 i ^ - 52 j ^ + 26 k ^ ∴ Direction Ratio of required plane = 1 , - 2 ,   1 ∴ Equation of required plane is x - 2 y + z = 0 .

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