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JEE Main2018MathematicsThree Dimensional GeometryActual

If L 1 is the line of intersection of the planes 2 x - 2 y + 3 z - 2 = 0 , x - y + z + 1 = 0 and L 2 is the line of intersection of the planes x + 2 y - z - 3 = 0 , 3 x - y + 2 z - 1 = 0, then the distance of the origin from the plane, containing the lines L 1 and L 2 is

Options

  1. A1 2
  2. B1 4 2
  3. C1 3 2
  4. D1 2 2

Correct answer

C. 1 3 2

Step-by-step solution

Direction Ratio's of the line L 1 i j k 2 - 2 3 1 - 1 1 = i 1 - j   - 1 + k ( 0 ) = 1 ,   1 ,   0 At y = 0 2 x + 3 z = 2 x + z = - 1 →   ( - 5 , 0 , 4 ) is point Equation of L 1 x + 5 1 = y 1 = z - 4 0 = α Similarly for L 2 x - 7 5 3 = y - 5 = z + 8 5 - 7 = β Point of intersection of L 1 and L 2 ( - 1 , 4 , 4 ) Direction Ratio's of normal to plane passing through L 1 and L 2 = i j k 1 1 0 3 - 5 - 7 = i - 7 - j - 7 + k - 5 - 3 = - 7 i + 7 j - 8 k = - 7 ,   7 ,  

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