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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A perpendicular is drawn from a point on the line x - 1 2 = y + 1 - 1 = z 1 to the plane x + y + z = 3 such that the foot of the perpendicular Q also lies on the plane x - y + z = 3 . Then the coordinates of Q are

Options

  1. A2 , 0 , 1
  2. B– 1 , 0 , 4
  3. C4 , 0 , – 1
  4. D1 , 0 , 2

Correct answer

A. 2 , 0 , 1

Step-by-step solution

Let point P on the line is 2 λ + 1 ,   - λ - 1 ,   λ The foot of perpendicular Q is given by x - 2 λ - 1 1 = y + λ + 1 1 = z - λ 1 = - 2 λ - 3 3 ∵   Q Lies on x + y + z = 3     &     x - y + z = 3 ⇒ x + z = 3     &     y = 0 y = 0 ⇒ λ + 1 = - 2 λ + 3 3 ⇒ λ = 0 ⇒ Q is 2 ,   0 ,   1

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