Now we are getting into questions of style, on which reasonable
persons may disagree.
In that spirit, let me offer an opinion about style, along with
some rationale.
I prefer to let plain old g represent a vector. In the rare
cases where I want the magnitude of g, I write |g| explicitly.
In contrast, books tend to use boldface *g* for the vector,
and plain g for the corresponding magnitude.
Rationale:
1) When writing on paper, or writing email, it is a pain
to write boldface symbols.
In this forum, we could perhaps write *g* or g_vec,
especially when we want to emphasize the vector character,
but still there is temptation (for students and everybody
else) to simplify.
2) We soon run out of typographical decorations. It's not
obvious how we should decorate matrices, bivectors, and
other higher-dimensional objects. Consider for example
R = 0.5 + dx ∧ dy
which is the sum of a scalar and a bivector. Hint: every
complex number can be written in this form. IMHO it is
not worth the trouble to boldface such things.
3) In my experience, the times that I want the vector g
vastly outnumber the times I want the magnitude |g|.
The effort required to write |g| is the least of my
worries.
4) Boldface *g* and plain g are too similar. Students
might always notice the distinction.
Nobody is obliged to do it this way. It's just a possibility
for you to consider.