\documentclass[10pt]{article}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.16}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}

\begin{document}



\begin{tikzpicture}[x=1cm,y=1cm]

\begin{axis}[
x=1cm,y=1cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-0.5,
xmax=6.5,
ymin=-1.5,
ymax=3.5,
xtick={-2,-1,...,7},
ytick={-3,-2,...,7},]

\clip(-2.362405497527683,-3.0044357261417667) rectangle (9.498720909947316,7.085904141701357);

\draw [-latex,line width=2pt,color=red] (0,0) -- (6,2);
\draw [-latex,line width=2pt, color=orange] (0,0) -- (1.5,3);
\draw [-latex,line width=2pt,color=blue] (0,0) -- (4.5,-1);
\draw [-latex,line width=1.2pt,dash pattern=on 1pt off 1pt,color=blue] (1.5,3) -- (6,2);
\draw [-latex,line width=1.2pt,dash pattern=on 1pt off 1pt,color=orange] (4.5,-1) -- (6,2);
\begin{scriptsize}


\draw[color=black] (2.9604321482296485,1.3910965423527197) node {$u$};


\draw[color=orange] (0.5,1.852129724268709) node {$\vec{x}$};
\draw[color=orange] (2.090755918706305,-0.18060748690633394) node {$w$};
\draw[color=orange] (4.175883264189984,2.5751135777278735) node {$a$};
\draw[color=orange] (5.1,0.8776732261280955) node {$\vec{x}'$};

\end{scriptsize}
\end{axis}

\end{tikzpicture}

\end{document}