Cross product

The cross product of two three-dimensional vectors a and b is a third vector a × b, perpendicular to the plane the two inputs span. Its magnitude equals |a||b|sin θ, where θ is the angle between them. The direction is fixed by the right-hand rule: curl the fingers from a to b, and the thumb points along a × b.

Unlike the dot product (which eats two vectors and returns a scalar), the cross product preserves direction — which is exactly what's needed for rotational physics. Torque τ = r × F, angular momentum L = r × p, and the magnetic force F = qv × B are all cross products. It is why a bicycle wheel's angular momentum points along its axle, why a spinning top precesses sideways when pushed, and why electromagnetic radiation carries momentum.