Unit Vector

A Vector of unit length. The unit vector $\hat{\bf v}$ having the same direction as a given (nonzero) vector v is defined by

$$\hat{\bf v} \equiv {{\bf v}\over \vert{\bf v}\vert},$$

where $\vert{\bf v}\vert$ denotes the Norm of ${\bf v}$, is the unit vector in the same direction as the (finite) Vector v. A unit Vector in the ${\bf x}_n$ direction is given by

$$\hat {\bf x}_n \equiv {{\partial{\bf r}\over\partial x_n} \over \left\vert{\partial {\bf r}\over \partial x_n}\right\vert},$$

where ${\bf r}$ is the Radius Vector.

See also Norm, Radius Vector, Vector