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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Image of line x - 2 3 = y - 1 1 = z - 1 - 4 in the plane x + y + z = 7 is

Options

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

Correct answer

C. x - 4 3 = y - 3 1 = z - 3 - 4

Step-by-step solution

The line is perpendicular to normal, hence the line is parallel to plane, so the reflected line has the same direction. Now, image of 2,1 , 1 in the plane is α , β , γ say, then α - 2 1 = β - 1 1 = γ - 1 1 = - 2 4 - 7 1 + 1 + 1 = 2 So, the point is 4,3 , 3

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