Blender has a tests file for the mathutils module.
Execute this from Blenders source code directory:
blender --background -noaudio --python source/tests/bl_pyapi_mathutils.py
This is a simple example of testing in Python and currently all tests pass,
BUT: We miss tests for mathutils.Vector
As well as testing for success, its useful to test that zero length vectors give correct exceptions with angle measurement and incomparable args fail properly.,
Vectors sized 4+ are now supported but not used by many functions which rely on 2d or 3d vectors only, so ensuring large vectors dont fail is important too.
This is more of a beginner testing task since you can use existing tests as a reference.
Note, for extra points, heres a crash that could have been found with testing.
rB06b6cd83459713ef5c00f705f6cdf1481ed24179 Vector.cross on vectors sized >4