Adjusting vectors with tikzpicture and pgfplots

Question

This is a follow-up question to this question. Thanks to the answers given there I have the following code now

\documentclass{beamer}
\usetheme{metropolis} % Use metropolis theme
\usepackage[english,ngerman]{babel} % the new way
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{pgfplots}
\usepackage{tikz}

\begin{document}
\begin{figure}[!htb]
        \vspace{-0.5cm}
        \centering
        \begin{tikzpicture}
        \begin{axis}[
        xmin=-6.067, xmax=6.433,
        ymin=-1.3,ymax=2.2,
        scatter/classes={a={mark=o,draw=black}},
        xlabel={$x$},
        ylabel={$y$},
        scale=0.9
        ]

        \addplot[scatter,only marks,mark size = 1pt,fill = red,scatter src=explicit symbolic]
        table {
            % some points go here...
        };

        \addplot [|->, thick,  black]
        coordinates { (0,0) (3,1)};

        \addplot [|->, thick,  black]
        coordinates { (0,0) (-0.3,1)};
        \end{axis}

        \end{tikzpicture}
    \end{figure}
\end{document}

producing this output (please note that the missing arrow of the second vector seems to be a result of the Overleaf PDF export and is actually present in the preview):

Now I would like to achieve the following:

1. I would like to remove the vertical line at the start point of each vector.
2. I would like to extend each vector such that they actually "touch" the axes of my plot (see the thin lines I added to the plot).

Any help is, as always, highly appreciated.

Answer 1

I actually managed to solved this by simply adding a scaling factor and additional vectors with opposite signs:

    [...]
    \addplot [-, thick,  black, dashed]
    coordinates { (0,0) (2.2*3,2.2*1)};

    \addplot [-, thick,  black, dashed]
    coordinates { (0,0) (2.2*-3,2.2*-1)};

    \addplot [-, thick,  black, dashed]
    coordinates { (0,0) (2.2*-0.3,2.2*1)};

    \addplot [-, thick,  black, dashed]
    coordinates { (0,0) (2.2*0.3,2.2*-1)};