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 P: 234 Rotating vectors on a unit sphere You want all the unit vectors (a circle's worth of them) that make a 120-degree angle with the given one? If your given vector is $(1,0,0)$, then the unit vectors with a 120-degree angle to that are parameterized by $(-1/2,(\sqrt3/2)\cos\theta,(\sqrt3/2)\sin\theta)$ for $0\le\theta<2\pi$. If you have a different given vector, just multiply everything by any rotation matrix that takes $(0,0,1)$ to the vector you were given.