Shortest distance between skew lines
Three-dimensional geometry and vector algebra · Mathematics
Study notes
Q: Lines: r = (1,0,0)+t(1,1,0) and r = (0,1,1)+s(1,−1,0). Skew? Shortest distance? d₁×d₂ = |i j k; 1 1 0; 1 −1 0| = (0,0,−2). a₂−a₁ = (−1,1,1). Dot with (0,0,−2): −2. d = |−2|/2 = 1. Check intersection: would need same point - the z's differ (0 vs 1 always). Skew ✓, distance 1.