A **unit vector** $u$ is a [[Vector]] whose [[vector length]] equals one. Then $u \cdot u=1$ To get a unit vector with the same direction as a vector $v$, divide it by its [[vector length|magnitude]] $\frac{\boldsymbol{v} }{\|\boldsymbol{v}\|}$ Standard notation for unit vectors in two dimensions $\boldsymbol{u}=\left[\begin{array}{l}\cos \theta \\ \sin \theta\end{array}\right] \qquad \boldsymbol{i}=\left[\begin{array}{l}1 \\ 0 \end{array}\right] \qquad \boldsymbol{j}=\left[\begin{array}{l}0 \\ 1\end{array}\right]$