This applet is designed to build intuition about cross products of 3-vectors. The vectors are controlled by sliders tied to the coordinates of the two vectors.

- The applet has a control window and 2 graphics windows.
- The first graphical window is the coefficient sliders window. Dragging the labeled dots will change the coefficients of the vectors U and V.
- The second graphical window is the cross product window. It
displays the vectors U and V, as well as the cross product vector
UxV. It also displays the parallelogram with U and V as
edges. The magnitude of UxV is the area of the parallelogram.

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

Things to notice:

- The cross product should be perpendicular to both U and V.
For any U and V 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 U and V are zero, then UxV is along the z-axis.

- Using the sliders swap U and V. What happens to UxV.

- What happens to UxV if both U and V 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.