# Components of a cross product

1. Aug 15, 2010

### zoner7

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?

Last edited: Aug 15, 2010
2. Aug 16, 2010

### ehild

I would write both v and w in Cartesian coordinates to do the vector product.

ehild

3. Aug 16, 2010

### zoner7

I would do that, but the magnitude of the magnus force is not equal to the cross product of the angular velocity and velocity vectors, it is only in that direction.

I need to multiply the magnitude (I have it) by a mess of trigonometric functions.

4. Aug 16, 2010

### Hurkyl

Staff Emeritus
If you are using the cross product to define a direction, then what does its magnitude have to do with anything?