---
title: Vector
tags: note vector math
created: 2023-08-29T11:59:28Z
published: true
---

## 2D

### Angle

```go
atan2(y, x)
```

### Cross

```go
x * y2 - y * x2
```

### Distance

```go
(a - b).Length()
```

### Dot

```go
x * x2 + y * y2
```

### From angle

```go
x = cos(angle)
y = sin(angle)
```

### Length

```go
sqrt(x * x + y * y)
```

### Normalize

```go
length := x * x + y * y

if length == 0 {
	return
}

length = sqrt(length)
x /= length
y /= length
```

## 3D

### Cross

```go
( y * z2 - z * y2,
  z * x2 - x * z2,
  x * y2 - y * x2 )
```

### Distance

```go
(a - b).Length()
```

### Dot

```go
x * x2 + y * y2 + z * z2
```

### Length

```go
sqrt(x * x + y * y + z * z)
```

### Normalize

```go
length := x * x + y * y + z * z

if length == 0 {
	return
}

length = sqrt(length)
x /= length
y /= length
z /= length
```