Editing Unit vector (section)

==Right versor==
A unit vector in <math>\mathbb{R}^3</math> was called a '''right versor''' by [[W. R. Hamilton]], as he developed his [[quaternion]]s <math>\mathbb{H} \subset \mathbb{R}^4</math>. In fact, he was the originator of the term ''vector'', as every quaternion <math>q = s + v</math> has a scalar part ''s'' and a vector part ''v''. If ''v'' is a unit vector in <math>\mathbb{R}^3</math>, then the square of ''v'' in quaternions is −1. Thus by [[Euler's formula]], <math>\exp (\theta v) = \cos \theta + v \sin \theta</math> is a [[versor]] in the [[3-sphere]]. When ''θ'' is a [[right angle]], the versor is a right versor: its scalar part is zero and its vector part ''v'' is a unit vector in <math>\mathbb{R}^3</math>.

Thus the right versors extend the notion of [[imaginary unit]]s found in the [[complex plane]], where the right versors now range over the [[2-sphere]] <math>\mathbb{S}^2 \subset \mathbb{R}^3 \subset \mathbb{H} </math> rather than the pair {{math|{''i'', −''i''}}} in the complex plane.

By extension, a '''right quaternion''' is a real multiple of a right versor.