Vectors [vb6]

I have two lines that represent movement vectors. They can each be of any direction or length. In one unit of time a point associated with that vector would move from the foot to the tail, obviously. As such, they both move at different speeds. I need to find the point in time where two points moving along the two vectors are seperated by a specific distance. I'm not so much concerned with the point in time though as I'm concerned with where on each vector the points are.

As an example.

Vector 1 has components (1,1)-(4,4)
Vector 2 has componenets (8,1)-(4,5)

As each point moves along each vector, there will be a certain moment when the points are exactly 2 units away from each other. How do I find that moment? Thanks.