Find the shortest distance the lines `vecr = hati+hatj+lambda(2hati-hatj+hatk)` and `vecr = (2 hati+hatj+hatk) - mu (3hati-5hatj)`

Explanation

`veca_(1) = hati+vecj, vecb_(1) = 2hati-hatj+hatk`
`veca_(2) = 32hati+hatj-hatk, vecb_(2) = 3hati-5hatj+2hatk]`
`veca_(2) - veca_(1)- (2hati+hatj-hatk) - (hati+hatj) = hati-hatk`
`vecb_(1)xxvecb_(2)=|{:(hati,hatj,hatk),(2,-1,1),(3,-5,2):}|`
`= hati(-2+5)-hatj(4-3)+hatk(-10+3)`
`=3hati-hatj-7hatk`
and `(vecb_(1) - vecb_(2))(veca_(2)-veca_(1)) = (3hati-hatj-7hatk).(hati-hatk)`
` = 3+7 = 10`
Therefore the shortest distance between two lines
`= |((vecb_(1) xx vecb_(2)).(veca_(2)-veca_(1)))/((vecb_(1)xxvecb_(2)))|`
`= |(10)/(sqrt(9+1+49))|= (10)/(sqrt(59))` units.