Rotating XYZ coordinates to a new Z axis.

I have XYZ coordinates of an object moving in space, but the XYZ axes are arbitrary. I have 2 XYZ points on a known Z line. how can I make my data correspond to the known Z axis and make sure that the XY plane is aligned accordingly?

[Jan]

The question is not clear yet. Are you looking for the 3D rotation matrix, which rotates one set of an orthogonal coordinate system to another one? To suggest a solution, it would be useful to edit your question and insert any details, e.g. how the "points" or "coordinates" are stored.