Here is the problem verbatim: The polar and azimuthal angles of a vector are Θ1 and Φ1. The polar and azimuthal angles of a second vector are Θ2 and Φ2. Show that the angle ϒ between the two vectors satisfies the relation: cos ϒ = cosΘ1*cos Θ2+sinΘ1*sinΘ2*cos(Φ1-Φ2) Hint: write out the Cartesian components of each vector in spherical coordinates and then evaluate the scalar product. Where I run in to trouble with this problem is when writing out the Cartesian components into Spherical components. I do know that x = ρ*sinΘ*cosΦ, y = ρ*sin Θ*sinΦ, and z=ρ cos Θ, but I'm not sure how to write a vector in the form of B= Bxx-hat+Byy-hat+Bzz-hat using the x, y, and z spherical components. Someone please point me in the right direction.