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I want to rotate vectors through 120 and they are unit vectors so they lie on a unit spheres. So basically the tails of the vectors are at the origin and given one vector with spherical coordinates (1,θ,∅), how do I obtain the coordinates of the unit vectors that make 120 degrees with the given vector?

I tried using the dot product relation. But it doesn't seem to work for all values of theta and phi I pick for the initial one b/c sometimes, I get cosine and sine values that are greater than one.

Is it because I'm missing some kind of subtlety in 3 dimensions?

Thanks!

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# Rotating vectors on a unit sphere

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