This worksheet is designed to build familiarity with the cross
product of two vectors in three space. This can be done with the
applets obtained by following either of the following links:

http://www.slu.edu/classes/maymk/banchoff/CrossProductSliders.html

http://www.slu.edu/classes/maymk/banchoff/CrossProductTextBox.html

(The difference between the two applets is in the method of
controlling the coordinates of the two vectors of which we are taking
cross products. One applet uses sliders while the other uses text
boxes. It is easier to get an exact value with text boxes.
It is easier to see movement and patterns with sliders.
Tastes will vary on which is easier.)

Spread windows
where you can see them all. Increase the size of the control
panel so that you can see all the readout boxes.

1) Find the cross product of (1,1, 0) and (-1,1,1). Find the
cross product of (1,-1,0) and (-1,1,1).

What happens if you reverse the order of the two vectors? What
happens if you double the size of the two vectors?

2) Set the first vector to (1,-1,0) and rotate the graph so that you
are looking at that vector head on. What has happened to the
rectangle bounded by the two vectors? What is the visual
relationship between the first vector and the cross product vector?

Move the second vector around and describe what happens to the cross
product vector.

3) Set the first vector to (1,1,1) and the second vector to (1,k,-1) for some value of k. Move k through a variety of values. Which value of k makes the cross product smallest? What can be said about the angle where the cross product is smallest?

Return to the SLU
Calculus Applet page.

Last updated By Mike May, S.J., September 18, 2006.