When using the llncs style from Springer this conflicts with the definition of \vec from amsmath. Thus this can be overcome with your own def:

\let\origvec\vec
\documentclass{llncs}
\let\springervec\vec
\let\vec\origvec
\usepackage{amsmath}
\begin{document}
$\vec{a}$ 
$\springervec{a}$
\end{document}