This applet is designed to build intuition about cross products of 3-vectors. The coordinates of V and W can be changes either by using the forward and back buttons to move them through the range of values or by entering values in the appropriate text box. The value in a text box does not have to be in the given range.

- The applet has a control window and a graphics window.
- The graphical window is the cross product window. It
displays the vectors V and W, as well as the cross product vector VxW. It also displays the parallelogram with V and W as
edges. The magnitude of VxW is the area of the parallelogram.

- The control window gives the coefficients of V, W, and VxW. It also gives the lengths of these vectors and the cosine of the angle between V and W.

Things to notice:

- The cross product should be perpendicular to both V and W.
For any V and W you can rotate the crossproduct window so that you are looking directly down U
or V. The parallelogram then become a line and the other two
vectors are perpendicular. If the z components of both V and W are zero, then VxW is along the z-axis.

- Using the text boxes swap V and W. What happens to VxW.

- What happens to VxW if both V and W are doubled?

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University. It is used with permission. Go to the Banchoff Applet Help page.

Return to the Banchoff Applet page.

Return to the SLU Calculus Applet page.

Return to the Saint Louis University Department of Mathematics and Computer Science home page

Last updated By Mike May, S.J. , October 6, 2006.