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JEE Main20199 Jan 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The equation of the line passing through - 4 , 3 , 1 , parallel to the plane x + 2 y - z - 5 = 0 and intersecting the line x + 1 - 3 = y - 3 2 = z - 2 - 1 is

Options

  1. Ax + 4 3 = y - 3 - 1 = z - 1 1
  2. Bx + 4 1 = y - 3 1 = z - 1 3
  3. Cx + 4 - 1 = y - 3 1 = z - 1 1
  4. Dx - 4 2 = y + 3 1 = z + 1 4

Correct answer

A. x + 4 3 = y - 3 - 1 = z - 1 1

Step-by-step solution

A variable point on line x + 1 - 3 = y - 3 2 = z - 2 - 1 is - 3 t - 1 , 2 t + 3 , - t + 2 ∴ D R of variable point & - 4 , 3 , 1 is - 3 t + 3 , 2 t , - t + 1 Since line is parallel to x + 2 y - z - 5 = 0 ∴ - 3 t + 3 + 4 t + t - 1 = 0 ⇒ t = - 1 ∴ D R of line is 6 , - 2 , 2 or 3 , - 1 , 1 ∴ Equation of line is x + 4 3 = y - 3 - 1 = z - 1 1

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