The vector product (or "cross product") of two vectors A and B is defined as:
The resulting vector C then has the cartesian components:
Cy = Az Bx - Ax Bz
Cz = Ax By - Ay Bx
The applet above lets you play with this concept. With the sliders on the right, you can adjust the lengths of the vectors, r, as well as their angles relative to the z-axis, theta, and x-axis, phi. The cross product is calculated automatically and then displayed. The whole operation works, of course, only in three spatial dimensions. To give a more precise indication of the location of the vectors in 3-d, we show their projections into the xy plane as well.