Vectors

[Rocko]

anyone have a clear definition of how to do a cross product?

[Galileo]

The cross-product \vec C of two vectors \vec A and \vec B is most conveniently defined by:
|\vec C|=|\vec A||\vec B|\sin(\theta)
where \theta is the angle between \vec A and \vec B.
This gives the magnitude of \vec C. The direction is given by the right-hand rule.

To calculate the cross product when you know the components,
it's usually easiest to form the symbolic 3X3 determinant:
\vec A=(A_x,A_y,A_z)
\vec B=(B_x,B_y,B_z)
\vec C = \left|
\begin{array}{ccc}
\hat x & \hat y &\hat z \\
A_x & A_y & A_z\\
B_x & B_y & B_z
\end{array}\right|

This follows from \hat x \times \hat y = \hat z (and the other possible product combinations of these unit vectors) and the distributivity of the cross product (which is tedious to prove IIRC).