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JEE Main2014MathematicsThree Dimensional GeometryActual

The image of the line x - 1 3 = y - 3 1 = z - 4 - 5 in the plane 2 x - y + z +3=0 is the line

Options

  1. Ax - 3 3 = y + 5 1 = z - 2 - 5
  2. Bx - 3 - 3 = y + 5 - 1 = z - 2 5
  3. Cx + 3 3 = y - 5 1 = z - 2 - 5
  4. Dx + 3 - 3 = y - 5 - 1 = z + 2 5

Correct answer

C. x + 3 3 = y - 5 1 = z - 2 - 5

Step-by-step solution

We first find the intersection of line ( L 1 ) with the plane. Any general point on line can be written as 3 k + 1 , k + 3 , - 5 k + 4 . Substituting in equation of plane P we get 2 ( 3 k + 1 ) - ( k + 3 ) + ( - 5 k + 4 ) + 3 = 0 Which gives 6 = 0 which is not possible. So, we conclude that the line is parallel to the plane. ∵ 6 - 1 - 5 = 0 ∴ The reflected line ( L 2 ) will also have the same direction ratios. i.e.,   ( 3 , 1 , -   5 ) . Consider the normal perpendicular to the plane and line.

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