# Rotating vectors on a unit sphere

1. Mar 2, 2012

### tut_einstein

Hi,

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!

2. Mar 3, 2012

### tut_einstein

Anyone? I would really appreciate some help!

3. Mar 3, 2012

### Office_Shredder

Staff Emeritus
Rotating them by 120 degrees around what axis?

4. Mar 3, 2012

### Tinyboss

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.

5. Mar 4, 2012

### tut_einstein

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.