Hi;

Let S^2 be a 2-dimensional unit sphere in R^3. Let u and v be two unit vectors in R^3 (so in S^2). We will define an operation on S^2 by u*v is a unit vector obtained by rotating a vector u along v by 180 degree (Pi).

Define stab(v)={u in S^2: u*v=v}. My question is find stab(v) where v is in S^2.

Thank you in advance