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



Reversing the Order of Operands

Cross product of u and v

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).