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JEE Main201910 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

On which of the following lines lies the point of intersection of the line, x - 4 2 = y - 5 2 = z - 3 1 and the plane, x + y + z = 2 ?

Options

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

Correct answer

B. x - 1 1 = y - 3 2 = z + 4 - 5

Step-by-step solution

A general point on the given line x - 4 2 = y - 5 2 = z - 3 1 = λ   can we taken as 2 λ + 4 ,   2 λ + 5 ,   λ + 3 If it also lies on the given plane then 2 λ + 4 + 2 λ + 5 + λ + 3 = 2 ⇒ 5 λ + 12 = 2 ⇒ λ = - 2 ⇒ Point of intersection is 0 ,   1 ,   1 , which lies on x - 1 1 = y - 3 2 = z + 4 - 5

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