Sorry again if this is a noobie post.

In R3, find the shortest distance between the lines:

l1 = x (2, -1, 3) + t(1, -1, 4)

l2 = x (1, 0, 1) + t(1, -1, 4)

Unless I am mistaken I would take vector 1 to be (1, -1, 4) and vector 2 to be (1, -1, 4) as well.

Using the equation distance = |P1P2 dot n| / ||n||

with n = cross product of vector 1 and vector 2

But when I do the cross product, I receive a value of 0.

Can anyone help steer me in the right direction.

I'm sorry if this is a trivial question, I have not taken math courses in a few years.

Thank you for your time.