# How to distinguish 4D and 3D vectors in handwriting?

Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting.

In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to implement similar distinguishing in handwriting?

In component notation, 3d and 4d vectors are usually distinguished using latin and greek letters respecitively, e.g. $u_i$ and $u_\mu$.
Moreover, four-vectors without indices are usually just written as $u$, whereas three-vectors are denoted $\vec u$, as you say. You'll hardly find $\vec u$ denoting a four-vector.
The option $\underline{u}$ is also commonly used. Here you can also add more and more underlines for tensors - the number of underlines reflect the number of indices. $|u\rangle$ would also be possible, although it's mostly used in a quantum mechanical context.
An additional option, particularly useful when you ALSO have 2D vectors (or higher dimensions) is to preface your vector's name with a subscript--e.g., ${}_{4}v$ and ${}_{3}v$, etc. It's also semi-common to use different symbols for your different metrics--$g_{ab}$ for the 4-metric, $\gamma_{ab}$ for the 3-metric and $q_{ab}$ for the 2-metric, for example. That way, you can distinguish the pullback of the 2-metric onto the 2-space from its representation in the 4-space through the index convention noted by Nick Kidman.