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

\begin{comment}


\end{comment}

\begin{document}

\begin{tikzpicture}[scale=1.5]

%    \draw[step=0.1, color=lightgray] (-5,-1.5) grid(6,5);
%    \draw [triangle 45-triangle 45] (-4.5,5.5) node (yaxis) [above] {$y$}|- (3.5,0) node (xaxis) [right] {$x$};
    \draw[-triangle 45] (-4.5,0) -- (5.5,0) node[right] {$x$};

     \foreach \x in {-4,-2,-1,1,3,4}
       \draw (\x cm,1pt) -- (\x cm,-1pt) node[anchor=north] {$\x$};

     \draw[-triangle 45] (0,-1) -- (0,4) node[above] {$y$};
         \foreach \y in {2}
         \draw (1pt,\y cm) -- (-1pt,\y cm) node[anchor=east] {$\y$};

%Vector a

    \draw [color=red, thick, -triangle 45](0,0) -- (2,3) node[midway,sloped,above] {$\vec a$};
    \draw [color=red, dashed, thin] (2,-0.1) -- (2,3);
    \draw [color=red, dashed, thin] (-0.1,3) -- (2,3);
        \node[red] at (2,-0.25) {$a_1$};
        \node[red] at (-0.25, 3) {$a_2$};
%Vector b

    \draw [color=green!65!black, thick, -triangle 45](0,0) -- (5,1) node[midway,sloped,above] {$\vec b$};
    \draw [color=green!65!black, dashed, thin] (5,-0.1) -- (5,1);
    \draw [color=green!65!black, dashed, thin] (-0.1,1) -- (5,1);
    \draw [color=green!65!black, thick, -triangle 45, dashed](2,3) -- (-3,2) ;
            \node[green!65!black] at (5,-0.25) {$b_1$};
            \node[green!65!black, left] at (-0.05,1) {$b_2$};
%Vector a b

    \draw [color=blue, thick, -triangle 45](0,0) -- (-3,2) node[midway,sloped,above] {$\vec a - \vec b$};
    \draw [color=blue, dashed, thin] (-3,-0.1) -- (-3,2);
    \draw [color=blue, dashed, thin] (-0.1,2) -- (-3,2);
    \draw [color=blue, thick, -triangle 45, dashed](5,1) -- (2,3) ;
            \node[blue, right] at (0,2) {$a_2-b_2$};
            \node[blue] at (-3,-0.25) {$a_1-b_1$};

%        \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]{$b_2$};


%    \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, 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}