3D Geometry

Let the line (x - 2)/3 =  (y - 1)/-5 =  (z - 2)/2 lie in the plane x + 3y - αz + β = 0. Then (α, β) equals

  1. (-5, 5)
  2. (5, -15)
  3. (-6, 7)
  4. (6, -17)

Answer

2 + 3 × 1 – α (–2) + β = 0

2α + β = –5 

3 – 15 – 2α = 0

2α = –12

The correct option is C.