\begin{pspicture}(-1,-2)(6,6)
\psset{xMin=0, xMax=5, yMin=0, yMax=5, zMin=0, zMax=5, spotY=30, Alpha=150, yThreeDunit=1, IIIDticks, Dx=1, Dy=1, Dz=1}
\pstThreeDCoor[]

%\pstThreeDDot[drawCoor=true](3,3,4)
\def\xSchnittp{3,0,0}
\def\ySchnittp{0,3,0}
\def\zSchnittp{0,0,4}
\def\xyzSchnittp{3,3,4}
\pstThreeDCoor

\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](\zSchnittp)(3,0,4)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](3,0,4)(\xyzSchnittp)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](\xSchnittp)(3,0,4)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](\zSchnittp)(0,3,4)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](\ySchnittp)(0,3,4)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](0,3,4)(\xyzSchnittp)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](\xSchnittp)(3,3,0)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](3,3,0)(\ySchnittp)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=blue](3,3,0)(\xyzSchnittp)

\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=red](3,0,0)(3, -0.4,0)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed, linecolor=red](0,3,0)(-0.4,3,0)
\pstThreeDLine[linewidth=0.1pt, linestyle=dashed,linecolor=red](0,0,4)(0,-0.4,4)


\pstPlanePut[plane =xz](3.1,3.1,4.1){\green Vektor}
\pstPlanePut[plane =xz](3.3,2.6,4.1){\green ("Pfeil") $\vec{a}$}


%\setkeys{psset}{arrows=->,arrowsize=0.2}
\pstThreeDLine[linecolor=green](0,0,0)(3,3,4)
%\pstThreeDPut(3,-0.4,0){3}
%\pstThreeDPut(-0.4,3,0){3}
%\pstThreeDPut(-0.4,0,4){4}
%\pstThreeDPut(

%\pscustom[linewidth=1.2pt,arrowscale=1.5]{
%   \code{/x 1 def 
%         /y 4 x 1 add ln mul def} 
%      \multido{\i=1+1}{4}{
%          \moveto(!x y) 
%          \psline{->}(!x x)(!x y) \closepath 
%          \psline{->}(!x y)(!y y) \closepath 
%          \code{/x y def 
%                /y 4 x 1 add ln mul def} 
%      } 
 
%}


\pstPlanePut[plane =xz](3,-0.8,0){\color{red}$a_1$}
\pstPlanePut[plane =yz](-0.6,3,0){\color{red}$a_2$}
\pstPlanePut[plane =yz](0,-1,4){\color{red}$a_3$}
\end{pspicture}