Inline underset spilling over to next line

Question

The underset of my "xdim" command is touching characters in the line underneath. How to correct?

\documentclass[12pt]{minimal}
\usepackage{amsmath}

\newcommand{\xdim}[1]{\underset{\textrm{vec}}{\textrm{dim}}\left(#1\right)}

\begin{document}
$\xdim{f}$ consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna al ali qua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
\end{document}

Answer 1

Defining dim as an operator allows for distinguishing between inline and display equations in the "traditional" way: Subscripts are set "on the side" with inline use, while set "underneath" when used inside a display.

\documentclass[12pt]{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath

\newcommand{\xdim}[1]{\underset{\textrm{vec}}{\textrm{dim}}\left(#1\right)}
\DeclareMathOperator*{\DIM}{dim}
\newcommand{\xxdim}[1]{\DIM_{\text{vec}}(#1)}

\begin{document}
$\xdim{f}$ consectetur adipisicing elit, $\xxdim{f}$ sed do 
eiusmod tempor incididunt ut labore et dolore magna al ali qua. 
Ut enim ad minim veniam, quis nostrud exercitation ullamco 
laboris nisi ut aliquip ex ea commodo consequat.
\[
  \xdim{f} \neq \xxdim{f}
\]
\end{document}

For this you require the starred version: \DeclareMathOperator*

Answer 2

If you wish to keep the general appearance as you provided in your MWE, with that close line spacing, I see two options, and I have employed them both here. First, I made the underset in \scriptscriptstyle to save on vertical space. Secondly, I used stackengine, rather than \underset, to minimize the undersetting gap, set here to 1pt.

\documentclass[12pt]{minimal}
\usepackage{stackengine}
\usepackage{amsmath}

\newcommand{\xdim}[1]{\stackMath\stackunder[1pt]{%
  \textrm{dim}}{\scriptscriptstyle\textrm{vec}}\left(#1\right)}

\begin{document}

$\xdim{f}$ consectetur adipisicing elit, sed do eiusmod tempor
incididunt ut labore et dolore magna al ali qua. Ut enim ad minim
veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea
commodo consequat.

\end{document}