Rotation of a random unit vector at a point in 3D space by an angle I have a scenario where I need rotate a vector ( unit vector) at a point in space by an angle along Z-axis. Is it possible to help me to understand a procedure to achieve this. I'm using vb.net programming to do this programattically. 

Here is the schematics for your understanding:
Rotation matrix | wikipedia.org in section that says "in three dimensions". It's the first search result when searching about rotating a vector about an axis. Let me know if you have any questions.

For your specific problem: bring the point P to the origin, then rotate the vector about the Z axis, then bring the point P back to its original location.