I’ve been asked what is the standard notation for vectors. I normally use loose notation, unless I need to write or review a formal piece, in which case I follow the APS style. See also here.

A vector should be represented by a letter, in boldface or with a right arrow on top.

A caret should be used to indicate a unit vector.

An inner product should be indicated by placing a dot between two letters representing vectors.

Note that Dirac Notation is a different animal.

The APS Style Guide has additional guidelines.