Game Math: Vector Cross Product Explained
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The cross product, denoted by the "X" symbol, differs from the dot product in the form of its result.
The dot product computes two vectors and outputs a scalar value.
The cross product, however, outputs a new vector.
This new vector has a direction perpendicular to the plane formed by the input vectors, and its magnitude equals the area of the parallelogram they define.
For example, taking the cross product of vectors a and b produces a new vector that is perpendicular to the ab plane and has a magnitude equal to that area.
(This is particularly useful for calculating 360-degree directional information.)
Unlike the dot product, the cross product is not commutative — operation order carries significant meaning.
Reversing the operation order flips the resulting vector's direction.
Additionally, the direction changes depending on whether you're using a left-handed or right-handed coordinate system.