Find the shortest distance between the lines.
`r=(hat(i)+2hat(j)+hat(k))+lambda(hat(i)-hat(j)+hat(k)) " and " r=(2hat(i)-hat(j)-hat(k))+mu(2hat(i)+hat(j)+2hat(k))`.

Find the shortest distance between the lines vec(r)=(hat(i)+2hat(j)+hat(k))+lamda(hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)-hat(j)-hat(k)+mu(3hat(i)-hat(j)+hat(k))

Find the shortest distance between the lines vec(r)=(4hat(i)-hat(j))+lamda(hat(i)+4hat(j)-3hat(k)) and vec(r)=(hat(i)-hat(j)+2hat(k))+mu(2hat(i)+3hat(j)-2hat(k))

Find the shortest distance between the lines vec(r)=hat(i)+hat(j)+lamda(2hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)+hat(j)-hat(k)+mu(3hat(i)-5hat(j)+2hat(k))

Find the shortest distance between the following lines vec(r)=hat(i)+hat(j)+lamda(hat(i)-hat(j)+hat(k)) and vec(r)=2hat(i)+hat(j)-hat(k)+mu(3hat(i)-4hat(j)+hat(k))

Find the shortest distance between the following lines vec(r)=-hat(i)+2hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k)) and vec(r)=hat(i)-hat(j)+2hat(k)+mu(-hat(i)+hat(j)+hat(k)) .

Find the shortest distance between the following lines vec(r)=hat(i)-hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k)) and vec(r)=3hat(i)-hat(j)-2hat(k)+mu(-hat(i)+2hat(j)+hat(k))