# Maths basics

## 3D Vectors

3D vectors have an `x`

component, a `y`

component and a `z`

component

### The length of a vector:

```
length(v) = sqrt(v.x^2 + v.y^2 + v.z^2)
```

The length of a vector can be obtained with the help of the pythagorean theorem.

### The direction of a vector

```
normalize(v) = v / length(v)
```

Like with numbers (aka 1D vectors) the direction of a vector can be calculated by dividing the vector by the length of the vector.

### The distance between two numbers

```
distance(a, b) = length(b - a)
```

### Dot product

The dot product of two vectors `a = [ax, ay, az]`

and `b = [bx, by, bz]`

is defined as

```
dot(a, b) = ax * bx + ay * by + az * bz
```