3D Geometry

The distance of the point (1,0,2) from the point of intersection of the line (x - 2)/3 = (y + 1)/4 = (z - 2)/12 and the plane x - y + z = 16 is 

  1. 13
  2. 8
  3. 3√21
  4. 2√14

Answer

Point of intersection is:

(3k + 2, 4k – 1, 12k + 2)

⇨ 3k + 2 – 4k + 1 + 12k + 2 = 16

⇨ 11k = 11

⇨ k = 1 and point is: 

(5, 3, 14)

Distance = √(16 + 9 + 144)  = √169 = 13

The correct option is A.