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JEE Main20206 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual

A plane P meets the coordinate axes at A , B and C respectively. The centroid of ∆ ABC is given to be 1 , 1 , 2 . Then the equation of the line through this centroid and perpendicular to the plane P is :

Options

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

Correct answer

C. x - 1 2 = y - 1 2 = z - 2 1

Step-by-step solution

Let A ( α , 0 , 0 ) , B ( 0 , β , 0 ) , C ( 0 , 0 , γ ) then G α 3 , β 3 , γ 3 ≡ ( 1 , 1 , 2 ) α = 3 , β = 3 , γ = 6 ∴ eequation of plane is x α + γ β + z γ = 1 ⇒ x 3 + y 3 + z 6 = 1 ⇒ 2 x + 2 y + z = 6 ∴ required line x - 1 2 = y - 1 2 = z - 2 1

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