## Disclaimer

This site as of now just a technology demonstration and its claims should not be taken as true (even though I myself am pretty confident they are)

## Definition

We shall define the cross product in terms of two properties we are interested in:

- Distributive:
- Orthogonal:

It is worth mentioning that given a pair of vectors in there exist an infinite amount of vectors that satisfy these properties, so it is also necessary to introduce the following relations between the basis vectors to properly define the cross product.

We introduce the Levi-Civita symbol to condense our calculations.

Based on this we may now derive a way to compute the cross product of two vectors