The normalized vector û of a non-zero vector u is the unit vector codirectional with u, i.e.,
where ||u|| is the norm (or length) of u. The term normalized vector is sometimes used simply as a synonym for unit vector.
As opposed to a general vector, which represents direction and magnitude, a unit vector just represents direction. The components are called direction cosines, because each is the cosine of the angle between the vector and one coordinate axis.
These are not always written with a hat; but it can generally be assumed that i, j, and k are unit vectors in most contexts. Very often these unit vectors are written as e1, e2 and e3 respectively.
Other coordinate systems, such as polar coordinates or spherical coordinates use different unit vectors; notations vary.de:Einheitsvektor fr:Vecteur unitaire he:וקטור יחידה nl:Eenheidsvector pl:Wersor pt:Vetor unitário sv:Enhetsvektor th:เวกเตอร์หนึ่งหน่วย zh:单位向量