How to determine rotation and translation between v1 and v2

Hi all,

Say I have two 3D vectors, v1 and v2.

How do I determine the rotation and translation that is needed to go from v1 to v2?

I know the 4D rotation/translation matrix. But I see no way to solve these equations with just the v1 and v2 as known.

I actually have 2 points that move in 3D space. The two points that define the vectors are linked together in that they always are at the same distance from each other. So it's like a stick in 3D space and I would like to follow the two end points in terms of (x,y,z) translation and yaw, pitch, and roll, but I only know that starting vectors (at t=0) and the end vectors (at t=1).

Thanks all,

Marco