The acute angle between the line `r=(hat(i)+2hat(j)+hat(k))+lamda(hat(i)+hat(j)+hat(k))` and the plane `r*(2hat(i)+hat(j)+hat(k))=5`

The angle between the line r=(hat(i)+2hat(j)-hat(k))+lamda(hat(i)-hat(j)+hat(k)) and the plane r*(2hat(i)-hat(j)+hat(k))=4 is

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 angle between the line vec(r)=2hat(i)-hat(j)+2hat(k)=2hat(i)-hat(j)+2hat(k) the plane vec(r)*(2hat(i)-hat(j)+hat(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 angle between the line: vec(r) = (hat(i) - hat(j) + hat(k) ) + lambda (2 hat(i) - hat(j) + 3 hat(k)) and the plane vec(r). (2 hat(i) + hat(j) - hat(k) ) = 4. Also, find the whether the line is parallel to the plane or not.