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