vector-triangle-inequality.tex

\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes, calc, shapes, arrows}
\usepackage{amsmath,amssymb}

\usepackage{xcolor}
\definecolor{xvectorcolor}{HTML}{77933C}

\begin{document}
\begin{tikzpicture}[font=\boldmath]
    \large

    % Points
    \coordinate (A) at (0,0) {};
    \coordinate (B) at (5,0) {};
    \coordinate (C) at (2,2) {};

    % Draw the triangle
    \path[fill=blue!10, fill=blue!5]  (A) -- (B) -- (C) -- (A);
    \draw[ultra thick, xvectorcolor, arrows={-latex}]  (A) -- (C) node[sloped,midway,above=-0.1cm] {$x$};
    \draw[ultra thick, blue!80,      arrows={-latex}]  (C) -- (B) node[sloped,midway,above=-0.1cm] {$y$};
    \draw[ultra thick, red!80, arrows={-latex},line cap=round]  (A) -- (B) node[sloped,midway,right=-0.3cm,above=-0.1cm] {$x+y$};
\end{tikzpicture}
\end{document}