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

Explanation

Here lines (i) and (ii) are passing through the points `vec(a_(1))=hati+2hatj+hatk and vec(a_(2))=2hati-hatj-hatk`, respectively, and are parallel to the vector `vec(b)=2hati+ahatj+2hatk`.
Hence, the distance between the lines using the formula is given by
`" "(|vecbxx(vec(a_(2))-vec(a_(1)))|)/(|vecb|)=(|{:(hati,,hatj,,hatk),(2,,1,,2),(1,,-3,,-2):}|)/(3)=(|4hati-6hatj-7hatk|)/(3)=(sqrt(16+36+49))/(3)=(sqrt(101))/(3)`