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\documentclass{article}
\begin{document}
$\alpha\vec{x} = \vec{x}\alpha$,\hfill$\alpha\beta\vec{x}
= \beta\alpha\vec{x}$,\hfill$(\alpha + \beta)\vec{x} = \alpha\vec{x} +
\beta\vec{x}$,\hfill $\alpha(\vec{x} + \vec{y})
= \alpha\vec{x} + \alpha\vec{y}$.\\
\hspace*{1.5em}$\vec{x}\vec{y} = \vec{y}\vec{x}$\hfill
but\hfill$\vec{x}\times\vec{y} =
-\vec{y}\times\vec{x}$,\hfill\hfill$\vec{x}\vec{y} = 0$\hfill for\hfill%
$\vec{x}\perp\vec{y}$,\hfill\hfill$\vec{x}\times\vec{y} = 0$,\hfill
for\hfill$\vec{x}\parallel\vec{y}$.
\end{document}