The pure math of the problem: I have two vectors, both of which are expressed in spherical coordinates. I know the magnitudes as well as the polar and azimuthal angles that express these vectors. In addition, I have a third vector. I only know the magnitude of this vector, and I need to find its components in Cartesian coordinates. I know that its direction is described by the cross-product of the first two vectors. The underlying physics: The two vectors that I know are the velocity and angular velocity vectors of a ball flying through the air. I am trying to find the Cartesian components of the Magnus force, which can be described by (w X v), where v is the velocity vector and w is the angular velocity In essence, this is a trigonometry problem; nevertheless, I have no idea how to solve it. can anyone lead me in the right direction?