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

\begin{comment}


\end{comment}

\begin{document}

\begin{tikzpicture}[scale=1.5]
    % Zeichne Grid
    %\draw[step=0.1, color=lightgray] (-1.5,-1.5) grid(8,6);
    % Draw axes
    \draw [triangle 45-triangle 45] (0,5.5) node (yaxis) [above] {$y$}|- (7.5,0) node (xaxis) [right] {$x$};

    \draw [color=red, thick, -triangle 45](0,0) -- (5,1) node[midway,sloped,above] {$\vec b$};
        \draw [color=red, dashed, thin] (5,-0.1) -- (5,1);% node[pos=-0.05]{$b_1$} ;
        \draw [color=red, dashed, thin] (-0.1,1) -- (5,1);% node[pos=-0.05]{$b_2$};
        \node[red] at (5,-0.25) {$b_1$};
        \node[red, left] at (-0.05,1) {$b_2$};
    \draw [color=red, thin, -triangle 45, dashed](2,4) -- (7,5);

    \draw [color=orange, thick, -triangle 45](0,0) -- (2,4) node[midway,sloped,above] {$\vec a$};
        \draw [color=orange, dashed, thin] (2,-0.1) -- (2,4);
        \draw [color=orange, dashed, thin] (-0.1,4) -- (2,4);
        \node[orange] at (2,-0.25) {$a_1$};
        \node[orange, left] at (-0.05,4) {$a_2$};
    \draw [color=orange, thin, -triangle 45, dashed](5,1) -- (7,5);

    \draw [color=blue, thick, -triangle 45](0,0) -- (7,5) node[midway,sloped,above] {$\vec a + \vec b$};
        \draw [color=blue, dashed, thin] (7,-0.1) -- (7,5); %node[pos=-0.025]{$a_1+b_1$} ;
        \draw [color=blue, dashed, thin] (-0.1,5) -- (7,5); %node[anchor=west, pos=-0.1]{\fbox{$a_2+b_2$}};
        \node[blue] at (7,-0.25) {$a_1+b_1$};
        \node[blue, left] at (-0.05,5) {$a_2+b_2$};


    \foreach \y in {0,3}
        \draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};

    \foreach \x in {0,3,6}
        \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};

     \node[right] at (3.0,5.5) (x) {Parallelogramm};

     \node[right,color=white] at (3.0,3.3) (y) {xx};

    \draw[-open triangle 45,gray] (x) .. controls +(down:1cm) and +(left:1cm) .. (y);

\end{tikzpicture}
\end{document}