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\documentclass[10pt,a5paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\newcommand{\myvec}[2]{({#1}_1,{#1}_2,\dots,{#1}_{#2})}
\newcommand{\myvecn}[1]{\myvec{#1}{n}}
\newcommand{\myvecopt}[2][n]{({#2}_1,{#2}_2,\dots,{#2}_{#1})}
\providecommand{\vec}[1]{\overleftarrow{#1}}
\begin{document}
\[
\vec{v}=\myvecopt{v}
\]
later...
\[
\vec{w}=\myvecopt[10]{w}
\]
\end{document}
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