\documentclass{article}
\usepackage{amsmath}
\makeatletter
% smallmatrix with left alignment
\newenvironment{lsmallmatrix}{\null\,\vcenter\bgroup
\Let@\restore@math@cr\default@tag
\baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
\ialign\bgroup$\m@th\scriptstyle##$\hfil&&\thickspace\hfil
$\m@th\scriptstyle##$\hfil\crcr
}{%
\crcr\egroup\egroup\,%
}
% smallmatrix with right alignment
\newenvironment{rsmallmatrix}{\null\,\vcenter\bgroup
\Let@\restore@math@cr\default@tag
\baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
\ialign\bgroup\hfil$\m@th\scriptstyle##$&&\thickspace\hfil
$\m@th\scriptstyle##$\hfil\crcr
}{%
\crcr\egroup\egroup\,%
}
\makeatother
% 3x1 smallmatrix with left alignment
\newcommand{\ltvect}[3]{%
\ensuremath{\Bigl(\negthinspace\begin{lsmallmatrix}#1\\#2\\#3\end{lsmallmatrix}\Bigr)}}
% 3x1 smallmatrix with right alignment
\newcommand{\rtvect}[3]{%
\ensuremath{\Bigl(\negthinspace\begin{rsmallmatrix}#1\\#2\\#3\end{rsmallmatrix}\Bigr)}}
% 3x1 smallmatrix with centered entries
\newcommand{\ctvect}[3]{%
\ensuremath{\Bigl(\negthinspace\begin{smallmatrix}#1\\#2\\#3\end{smallmatrix}\Bigr)}}
\begin{document}
Example of a smallmatrix with left alignment
$\begin{lsmallmatrix}
5\\-1000\\3\\2