Any plane through the second line is 22(2 + 3k) + (1 + k) +(1 + 2k) = 0 If this is parallel to the first line, then (2 + 3k) + (1 + k) + (1 + 2k) = 0 ⇒ = −
2
3
⇒ Plane is 2x + y + z - 1 −
2
3
(3x + y + 2z - 2) = 0 or y - z + 1 = 0 The required SD must be distance of this plane from any point on the line x = y = z say (1, 1, 1) ⇒ SD =