Why is the vector sign and "2" are too close? Never faced it before.....
I wrote: \vec{p}^2

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You won't have this problem with the esvect package:
\documentclass{article}
\usepackage{siunitx}
\usepackage[b]{esvect}
\begin{document}
\[ {\vec p}^2\qquad \vv p^2 \]%
\end{document}
Bernard
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$\vec{p}^{\,2}$– JLDiaz Oct 10 '15 at 18:28\vec{{}p}^{2}looks definitely better. – Manuel Oct 10 '15 at 20:26