\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=1.5]
%\begin{tikzpicture}[scale=3]

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

    \draw[help lines] (0,0) grid (7,3);
    \draw[-triangle 45] (0,0) -- (4,0) node[midway,sloped,above] {$\vec a$};
    \draw[-triangle 45] (0,0) -- (2,2) node[midway,sloped,above] {$\vec b$};

    \draw[style=dashed]  (2,2) -- (6,2);
    \draw[style=dashed]  (4,0) -- (6,2);
    
    
    \draw (0,0) +(0:1cm) arc (0:45:1cm);

    \path (0,0) ++(22.5:.75cm) node{$\alpha$};

\end{tikzpicture}
\end{document} 