3D Geometry

If the lines (x - 1)/2 = (y + 1)/2 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1 intersect, then k is equal to

  1. 9/2
  2. 2/9
  3. -1
  4. 0

Answer

Any point on (x-1)/2 = (y + 1)/2 = (z - 1)/4 = t is (2t + 1, 3t - 1, 4t + 1)

Any point on (x - 3)/1 = (y - k)/2 = z/1 = s is (s + 3, 2s + k, s)

Given lines are intersecting, t = -3/2 and s = -5

The correct option is A.