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Rotating vectors on a unit sphere

  1. Mar 2, 2012 #1

    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?

  2. jcsd
  3. Mar 3, 2012 #2
    Anyone? I would really appreciate some help!
  4. Mar 3, 2012 #3


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    Rotating them by 120 degrees around what axis?
  5. Mar 3, 2012 #4
    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 [itex](1,0,0)[/itex], then the unit vectors with a 120-degree 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.
  6. Mar 4, 2012 #5
    I need to rotate about the origin. I'm not sure what the axis is.

    Also, tinyboss, I don't quite understand your answer. I know how to do it in 2 dimensions (when theta = pi/2, wheer theta is theta is the polar angle of spherical coordinates - angle made with the z-axis that is).

    But when I move off the xy plane I don't know how to find the unit vectors that are 120 degrees apart from the given one.
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