normalized vector or versor \boldsymbol{\hat{u}} of a non-zero vector \boldsymbol{u} is the unit vector codirectional with \boldsymbol{u}, i.e., \boldsymbol{\hat{u}} = \frac{\boldsymbol{u}}{\|\boldsymbol{u}\|} where \|\boldsymbol{u}\| is the norm (or length) of \boldsymbol{u}. The term normalized vector is sometimes used as a synonym for unit vector . The elements of a basis are usually