\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\usepackage{verbatim}

\tikzstyle{mybox} = [draw=red, fill=blue!20, very thick,
    rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]

\begin{document}

\begin{tikzpicture}[scale=1.2]
%\begin{tikzpicture}[scale=3]

    %\draw[step=0.1, color=lightgray] (-1,-1) grid(4.5,4.5);

   % \draw[help lines] (0,0) grid (4,4);

    \draw[-triangle 45] (0,0) -- (4,0) node[right] {$x$};

     \foreach \x in {1,2,3}
       \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};

     \draw[-triangle 45] (0,0) -- (0,4) node[above] {$y$};

     \foreach \y in {1,2,3}
         \draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};

     \draw [color=blue, thick, -triangle 45](0,0) -- (1,3) node[sloped,above] {$\vec b$} ;
     \draw [color=red, thick, -triangle 45](0,0) -- (3,1) node[right] {$\vec a$} ;

    \draw (0,0) +(19:25mm) arc (19:71:25mm);
    
    \draw (0.5,1) node[right, text width=15mm]{$\alpha \left ( \vec a, \vec b \right )$};

\end{tikzpicture}
\end{document}