Find the minimum distance between the line whose vector equations are
`vec r=(hat i +2 hat j+3hat k)+lambda(2 hat i+3 hat j+4 hat k)` and `vec r=(2 hat i+4 hat j+5 hat k)+ mu (4 hat i+6 hat j+8 hat k)`

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

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

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

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

Shortest distance between the lines: vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+u(2hat i+4hat j-5hat k)

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by: vec(r) = (3 hat(i) + 8 hat(j) + 3 hat(k) ) + lambda (3 hat(i) - hat(j) + hat(k)) and vec(r) = (-3 hat(i) - 7 hat(j) + 6 hat(k)) + mu (-3 hat(i) + 2 hat(j) + 4 hat(k)) .

Find the distance between the lines L_(1) and L_(2) given by : vec(r) = hat(i) + 2 hat(j) - 4 hat(k) + lambda (2 hat(i) + 3 hat(j) + 6 hat(k)) and vec(r) = 2 hat(i) + 3 hat(j) - 5 hat(k) + mu (2 hat(i) + 3 hat(j) + 6 hat(k)) .

Find the angle between the lines vec r*(hat i+2hat j-hat k)+lambda(hat i-hat j+hat k) and the plane vec r*(2hat i-hat j+hat k)=4