The shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) is

1. Connecting vector a₂ - a₁ = (1, 2, 2). 2. b₁ × b₂ = (3·5 - 4·4, 4·3 - 2·5, 2·4 - 3·3) = (-1, 2, -1). 3. |b₁ × b₂| = √(1+4+1) = √6. 4. Scalar triple product: 1(-1) + 2(2) + 2(-1) = -1+4-2 = 1. Distance = |1|/√6 = 1/√6. _Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.5.1_