Rotating vectors on a unit sphere
You want all the unit vectors (a circle's worth of them) that make a 120degree angle with the given one? If your given vector is [itex](1,0,0)[/itex], then the unit vectors with a 120degree angle to that are parameterized by [itex](1/2,(\sqrt3/2)\cos\theta,(\sqrt3/2)\sin\theta)[/itex] for [itex]0\le\theta<2\pi[/itex].
If you have a different given vector, just multiply everything by any rotation matrix that takes [itex](0,0,1)[/itex] to the vector you were given.
