# Unit vector

A unit vector is a vector whose magnitude is $1$.

The unit vector in the same direction as vector $\mathbf{r}$ is $\dfrac{\mathbf{r}}{|r|}$. It is sometimes written as $\hat{\mathbf{r}}$.

By convention, we often define three unit vectors, $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ to be parallel to the $x$, $y$ and $z$ coordinate axes.

So in column notation, $\mathbf{i}=\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}$, $\mathbf{j}=\begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$ and $\mathbf{k}=\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$.