# Unit vector

vector of length one

A unit vector is any vector that is one unit in length.

Unit vectors are often notated the same way as normal vectors, but with a mark over the letter (e.g. ${\displaystyle \mathbf {\hat {a}} }$ is the unit vector of a.)

To make a vector into a unit vector, divide it by its length: ${\displaystyle {\widehat {u}}=u/\lVert u\rVert }$

## In component form

Three common unit vectors used in component form are ${\displaystyle \mathbf {\hat {i}} }$ , ${\displaystyle \mathbf {\hat {j}} }$  and ${\displaystyle \mathbf {\hat {k}} }$ , referring to the unit vectors for the x-, y- and z-axes respectively. They are commonly just notated as i, j and k.

They can be written as the following: ${\displaystyle \mathbf {\hat {i}} ={\begin{bmatrix}1&0&0\end{bmatrix}},\,\,\mathbf {\hat {j}} ={\begin{bmatrix}0&1&0\end{bmatrix}},\,\,\mathbf {\hat {k}} ={\begin{bmatrix}0&0&1\end{bmatrix}}}$