## Cross Product

The definition of the cross product is:

... where is the Levi-Civita Symbol.

### Where does the angle come from?

First, there is an identity connecting the cross product to the scalar product:

So the identity is:

If the vectors **c** and **a** are the same and the vectors **d** and **b** are the same, it follows:

Hence the angle in the cross product comes from the angle in the scalar product:

## Scalar Product

Given a triangle with sides **a** and **b** and **c**=**b**-**a**, the Law of Cosines says:

On the other hand, using *only* the scalar product distributivity:

So since , it follows that: