Currently, I am trying to rotate a vector around another point. So if I have one point at, let's say (0, 5, 1) and another point at (10, 21, 6), I would try to rotate the second point, about 45 degrees around the first point. Quaternion.Euler seems like the way to go, but I haven't had any luck getting it to work. Is there any chance someone could post an example or something?

You should take a look at Transform.RotateAround >> http://docs.unity3d.com/Documentation/ScriptReference/Transform.RotateAround.html

1.translate so that the pivot is at origin 2. rotate the vector point around the origin with someQuaternion*someVector 3. translate back the same amount