# Cross products and the Hodge star operator

## Cross products

### The cross product

\(v\times u\)

#### Cross product is a bilinear map

This is a bilinear map from two vectors in \(\mathbb{R}^3\) to another vector in the same space.

\(V\times V \rightarrow V\)

#### Calculating the cross product

This is calcualted by:

\(u\times v=||u|| ||v|| \sin(\theta )n\)

The resulting vector is perpendicular to both input vectors.

## The Hodge star operator

### Introduction