Cross Product

Cross Product

The vector product of $$\vec a$$ and $$\vec b$$ is:

$$\vec a\times\vec b=|\vec a||\vec b|\sin\theta\,\hat n$$

where $$\hat n$$ is perpendicular to both vectors.

Terminology

- Cross product: Vector operation whose result is perpendicular to both input vectors.

- $$\hat n$$: Unit vector perpendicular to the plane containing $$\vec a$$ and $$\vec b$$.

Usage

- Used for area, torque, angular momentum, and perpendicular vectors.