Expressing vector as sum of rectangular components?

Question

Would it be possible to create a new command say \rvec that takes a variable number of arguments like \rvec{a}{b} and produces something like ai(hat) + bj(hat) and also \rvec{a}{b}{c} and produces ai(hat) + bj(hat) + ck(hat) ? I have a command that allows me to change the style of vector (arrow or bold face) so would it be possible to implement something like that so I can change the hats to arrows ? Any suggestion is welcome.

Answer 1

\documentclass{article}
\usepackage{etoolbox,amsmath}
\newcounter{ijk}
\newcommand{\ijk}{% Set each vector component
  \ifcase\value{ijk}\or
    \vecstyle{\text{\i}}\or% 1
    \vecstyle{\text{\j}}\or% 2
    \vecstyle{\text{k}}\else% 3
    ?
  \fi
}
\newcommand{\vecstyle}{\hat}
%\newcommand{\vecstyle}{\textbf}% Since i, j and k are set as text
%\newcommand{\vecstyle}{\vec}
\newcommand{\insertoperator}{}% Initialise operator between components
\newcommand{\rvec}[1]{% \rvec{<csv list>}
  % Using a cunning trick: https://tex.stackexchange.com/a/89187/5764
  \renewcommand{\insertoperator}{\renewcommand{\insertoperator}{+}}% Reinitialise operator to be delayed
  \setcounter{ijk}{0}% Reset ijk counter
  \renewcommand*{\do}[1]{% How each element in the <csv list> is processed
    \stepcounter{ijk}% Step ijk
    \insertoperator ##1\ijk}% Insert operator, argument and then the vector
  \expandafter\docsvlist\expandafter{#1}% Process the entire <csv list>
                                        % \expandafters here allow for passing macros
}
\begin{document}
$\rvec{a,b}$
$\rvec{a,b,c}$
$\rvec{a}$
\end{document}

With a bold vector format:

With a \vec vector format: