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 \(\mathbf{k}=\begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}\).