What angle between u and v will maximize their cross product?
Review: To reverse the direction of a vector w, scale it by -1. In other words, w and -w are colinear but 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
The magnitude of v × u is | v | | u | sin θ   =
|u||v| sin θ.
So, u × v = -(v × u) .