'the path of the tip of rotated vectors' or 'paths on a sphere'

I need to plot the path the tip of a specific vector draws,
when the vector is rotated around certain axis for some angels

as a basic example:
start vector is (0,0,1)
rotation around axis (0,1,0) for an angle of (pi/2)
rotation around axis (0,0,1) for an angle of (pi)

so the path should show something like starting at the bottom,
go up to the equator plane and then turn around the equator
to the other side

this could also be expressed in terms of a point moving on
a sphere ...

a graphical example would be like the path C in this figure
http://physics.aps.org/view_image/2213/medium/4

does anyone happen to know how i could easily implement something
like that?

with best regards
and thanks for your help/suggestions
  q

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