\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) -- (3,3) node[midway,sloped,above] {$\vec a$} ;
     \draw [color=blue, dashed, thin] (0,3) -- (3,3);
     \draw [color=blue, dashed, thin] (3,0) -- (3,3);

    \draw[snake=brace, mirror snake, color=red] (0,-0.1) -- (3,-0.1) node[midway,sloped,below] {$a_1$};
    \draw[snake=brace, mirror snake, color=green!65!black] (3.1,0) -- (3.1,3) node[midway, right] {$a_2$};
    \draw [fill=black](2.8,0.2) circle (0.25mm);

    \draw (0.1,3.5) node[right, text width=55mm, color=orange](y){L\"ange $\sqrt{a_1^2+a_2^2}$ nach Pythagoras};

    \draw[->,orange] (y) .. controls +(down:1cm) and +(up:1cm) ..  (2,2);

   % \draw[draw=green!50!black] (3,0) -- (3mm,0mm) arc (3:90:3mm); %-- cycle;
   \draw (3,0) +(90:5mm) arc (90:180:5mm);
\end{tikzpicture}
\end{document}