In Euclidean space, the dot product of two unit vectors is simply the cosine of the angle between them. This follows from the formula for the dot product, since the lengths are both 1.

The *normalized vector* of a non-zero vector **v** is the unit vector codirectional with **v**, i.e.,

The elements of a basis are often chosen to be unit vectors. In the 3-dimensional Cartesian coordinate system, these are usually **i**, **j**, **k**, unit vectors along the x, y , z axes respectively. Thus:

Other co-ordinate systems, such as polar coordinates or spherical coordinates use different unit vectors; notations vary.