[This] is a very nice Java applet that allows you to see what a cross product is. The applet shows A x B = C (i.e. C is the cross product of A and B) in 3 dimensions. You can drag A and B around to see the effects on C.

This UI is an example of very good interactivity. It makes it very easy for the user to see what happens and since its interactive, the feedback is instant and a little playing around with it gives the user an intuition of how cross products work (not how they are done).

Instead of a program where you enter numbers, dragging arrows around give you a much better view of whats going on, and allows the user to relate a real-life situation to it better too.