# Rotating a Unit Vector in 3D Using Quaternions

Initializing live version

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

A quaternion is a vector in with a noncommutative product (see [1] or Quaternion (Wolfram *MathWorld*)). Quaternions, also called *hypercomplex* *numbers*, were invented by William Rowan Hamilton in 1843. A quaternion can be written or, more compactly, or , where the noncommuting unit quaternions obey the relations .

Contributed by: Gerard Balmens (February 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Reference

[1] Wikipedia. "Quaternions and Spatial Rotation." (Feb 9, 2016) en.wikipedia.org/wiki/Quaternions_and_spatial _rotation.

## Permanent Citation