Use the cross product in three dimensions

THE IDEA

Read the example.

For two three-dimensional vectors, the cross product is perpendicular to both. Its direction follows the right-hand rule; its magnitude is the area of their parallelogram. The example varies the angle between two unit vectors in a plane.

‖u × v‖₂ = ‖u‖₂‖v‖₂ |sin θ|

Use it well

The three-dimensional cross product is not a replacement for the dot product in an arbitrary feature space. Dot products measure alignment; cross products encode a different geometric object.