Find the shortest distance between the following lines :
(i) `vecr=4hati-hatj+lambda(hati+2hatj-3hatk)` and
`vecr=hati-hatj+2hatk+mu(2hati+4hatj-5hatk)`
(ii) `vecr=-hati+hatj-hatk+lambda(hati+hatj-hatk)` and
`vecr=hati-hatj+2hatk+mu(-hati+2hatj+hatk)`
(iii) `(x-1)/(-1) = (y+2)/(1) = (z-3)/(-2)` and
`(x-1)/(1) = (y+1)/(2) = (z+1)/(-2)`
(iv) `(x-1)/(2) = (y-2)/(3) = (z-3)/(4)` and `(x-2)/(3) = (y-3)/(4) = (z-5)/(5)`
(v) `vecr = veci+2hatj+3hatk+lambda(hati-hatj+hatk)` and
`vecr = 2hati-hatj-hatk+mu(-hati+hatj-hatk)`

Answer

(i) `(6sqrt(5))/(5)`, (ii) `(5sqrt(2))/(2)` , (iii) `(8)/(sqrt(29))`
(iv) `1/(sqrt(6))` , (v) `sqrt(26)`