In a realistic city model, a metro track and a road above it are straight lines represented by i ̂-2j ̂+2k ̂+λ(i ̂+2j ̂-3k ̂ ) and 2i ̂-2j ̂+3k ̂+μ(-i ̂+j ̂+2k ̂ ) respectively.
Find the shortest distance between the metro track and the road, in the model. Show your work.