If the line, x - 3 1 = y + 2 - 1 = z + λ - 2 lies in the plane, 2 x - 4 y + 3 z = 2 , then the shortest distance between this line and the line, x - 1 12 = y 9 = z 4 is

Step-by-step solution

The points 3 ,   - 2 ,   -λ lie on Plane 2 x - 4 y + 3 z - 2 = 0 ⇒ 6 + 8 - 3 λ - 2 = 0 ⇒ 3 λ = 12 ⇒ λ = 4 Now, x - 3 1 = y + 2 - 1 = z + 4 - 2 ....... i x - 1 12 = y 9 = z 4 ........ i i Shortest distance formula d = x 1 - x 2 y 2 - y 1 z 2 - z 1 a 1 a 2 a 3 b 1 b 2 b 3 i ^ j ^ k ^ a 1 a 2 a 3 b 1 b 2 b 3 Calculating we get the value as 0 Hence lines are intersecting (As b → ∦ d → ) ∴ Shortest distance   = 0