Unit vector

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. $\mathbf {\hat {a}}$ is the unit vector of a.)

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

In component form

Three common unit vectors used in component form are $\mathbf {\hat {i}}$, $\mathbf {\hat {j}}$ and $\mathbf {\hat {k}}$, 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: $\mathbf {\hat {i}} ={\begin{bmatrix}1&0&0\end{bmatrix}},\,\,\mathbf {\hat {j}} ={\begin{bmatrix}0&1&0\end{bmatrix}},\,\,\mathbf {\hat {k}} ={\begin{bmatrix}0&0&1\end{bmatrix}}$