Consider the lines L_1 : {x+1}/3 = {y+2}/1 = {z+1}/2 L_2 : {x-2}/3 = {y+2}/2 = {z-3}/3

Unit vector perpendicular to both L_1 & L_2 is {-i^{-}-7j^{-}+5k^{-}}/{5\sqrt3}

Shortest distance between L_1 & L_2 is {17\sqrt2}/\sqrt3

Shortest distance between L_1 & L_2 is \frac{17\sqrt2}{5\sqrt3}