Find the distance between the parallel lines `vec(r)=hat(i)+2hat(j)-4hat(k)+m(2hat(i)+3hat(j)+6hat(k)) " and " vec(r)=3hat(i)+3hat(j)-5hat(k)+n(2hat(i)+3hat(j)+6hat(k))`

Find the angle between the pair of lines vec(r)=3hat(i)+5hat(j)-hat(k)+lambda(hat(i)+hat(j)+hat(k))" and "vec(r)=7hat(i)+4hat(k)+mu(2hat(i)+2hat(j)+2hat(k))

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 following pairs of lines : vec(r)=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) " & " vec(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k)) Note : Angle between two lines is the angle between vec(b_(1)) " and " vec(b_(2))

Find the angle between the following pairs of lines : r=3hat(i)+hat(j)-2hat(k)+lambda(hat(i)-hat(j)-2hat(k)) " and " r=2hat(i)-hat(j)-56hat(k)+mu(3hat(i)-5hat(j)-4hat(k)) .

Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) r=5hat(i)-4hat(k)+mu(3hat(i)+2hat(j)+6hat(k))

Find the angle between the following pairs of lines : r=2hat(i)-5hat(j)+hat(k)+lambda(3hat(i)+2hat(j)+6hat(k)) " and " r=7hat(i)-6hat(k)+mu(hat(i)+2hat(j)+2hat(k))

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

Find the sum of vectos a = hat(i)- 2hat(j)+hat(k),b=-2hat(i)+4hat(j)+5hat(k) and c=hat(i)-6hat(j)-7hat(k) .

Find the shortest distance between two lines whose vector equations are vec(r) = (hat(i) + 2 hat(j) + 3 hat(k))+lambda(hat(i)- 3hat(j) + 2 hat(k)) and vec(r) = (4 hat(i) + 5 hat(j) + 6 hat(k))+ mu (2 hat(i)+3 hat(j) + hat(k)) .

Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )