What angle between **u** and **v** will *maximize*
their cross product?

90°

*Review:*
To reverse the direction of a vector **w**, scale it by -1.
**w** and **-w**
point in opposite directions.
The diagram shows two cross products, their orientation
determined by the right hand rule.

The magnitude of **u** **×** **v**
is |**u**||**v**|
sin θ = **v**||**u**| sin θ.

So, **u** **×** **v** = -(**v** **×** **u**) .

Here is a really good interactive applet that demonstrates the dot product:

The Vector Cross Product - A JAVA Interactive Tutorial (Off-site applet.)

Keep this applet open as you read the following pages.

Does
-(**v** **×** **u**) = -**v** **×** **u** ?
(Decide this by looking at the diagram and visualizing both sides of the equation).