# Game Mathematics: Vectors, Rotations, and Transforms
Status: public
Confidence: medium (0.725) (verified)
Last verified: 2026-05-28
Generation: ai_assisted


## TL;DR

Game mathematics centers on vectors, rotations, and transformation matrices that express object positions and motion in game worlds.

## Core Explanation

Vectors, quaternions, and matrices give programmers a common vocabulary for position, direction, orientation, and coordinate-space transforms.

## Source-Mapped Facts

- Unity Vector3 represents 3D vectors and points, including common operations for positions, directions, and distances. ([source](https://docs.unity3d.com/ScriptReference/Vector3.html))
- Unity Quaternion represents rotations and is used to store and manipulate object orientation. ([source](https://docs.unity3d.com/ScriptReference/Quaternion.html))
- Unity Matrix4x4 is a 4x4 transformation matrix for translation, rotation, scale, shear, and perspective transformations using homogeneous coordinates. ([source](https://docs.unity3d.com/ScriptReference/Matrix4x4.html))

## Further Reading

- [Unity Scripting API: Vector3](https://docs.unity3d.com/ScriptReference/Vector3.html)
- [Unity Scripting API: Quaternion](https://docs.unity3d.com/ScriptReference/Quaternion.html)
- [Unity Scripting API: Matrix4x4](https://docs.unity3d.com/ScriptReference/Matrix4x4.html)