Find the shrotest distance between the lines `vecr = hati+hatj+ lambda(2hati-hatj+hatk)` and `vecr= 2hati+hatj-hatk+mu(2hati-hatj+hatk)`.

Explanation

Given lines are parallel
Here `veca=hati+hatj, veca_(2) = 2hati+hatj+hatk` and `vecb=2hati-hatj+hatk`
Now`veca_(2)-veca_(1) = (2hati+hatj-hatk) - (hati+hatj) = hati-hatk`
`vecb xx (veca_(2) - veca_(1)) = |{:(hati,hatj,hatk),(2,-1,1),(1,0,-1):}|`
`= hati(1-0)-hatj(-2-1)+hatk(0+1)`
`= hati+3hatj+hatk`
`|vecbxx(veca_(2)-veca_(1))| = sqrt(1+9+1) = sqrt(11)`
`|vecb| = sqrt(4+1+1) = sqrt(16)`
Shortest distance betwene the parallel lines
`= |(vecbxx(veca_(2) - veca_(1)))/(vecb)| = sqrt((11)/(6)) = (sqrt(66))/(6)` units.