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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The equation of the projection line of the line x + 1 2 = y + 1 - 1 = z + 3 4 on the plane x + 2 y + z = 6 is

Options

  1. Ax - 1 4 = y - 3 7 = z - 1 10
  2. Bx - 1 - 4 = y + 3 7 = z - 1 10
  3. Cx - 1 4 = y - 3 - 7 = z + 1 10
  4. Dx + 3 4 = y - 2 7 = z - 7 - 10

Correct answer

C. x - 1 4 = y - 3 - 7 = z + 1 10

Step-by-step solution

From the diagram, Coordinates of the point A are 2 λ - 1 , - λ - 1 , 4 λ - 3 (from the line) It must satisfy the equation of the plane 2 λ - 1 - 2 λ - 2 + 4 λ - 3 = 6 ⇒ λ = 3 So, coordinates of the point A are 5 , - 4,9 Point B ′ must be the foot of perpendicular for point B x + 1 1 = y + 1 2 = z + 3 1 = - - 1 - 2 - 3 - 6 1 + 4 + 1 = 2 x = 1 , y = 3 , z = - 1 Direction ratios of < A B ' > = < 4 , - 7 , 10 > So, the equation of projection of line is x - 1 4 = y - 3 - 7 = z + 1 10

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