Versor

$.. \| v\| ..$

In mathematics, a versor is a quaternion of norm one (a unit quaternion).

$q=e^{ar}=cos (a) + r sin (a)$

$r^2=-1$

r is a unit-length vector quaternion.

If $a= \dfrac {\pi}{2}$ then the versor is a right versor.

Hamilton defined a quaternion as the quotient of two vectors. A versor can be defined as the quotient of two unit vectors.

The norm of a versor is always equal to one.

The versor of a vector is the vector divided by the norm of the vector:

$\overrightarrow v$

$\hat v = \dfrac {1} {\| v\|}$

$\hat v = \dfrac {\overrightarrow v} {\| v\|}$