vplot = VectorPlot[{-3*x1+Sqrt[2]*x2,Sqrt[2]*x1-2*x2},{x1,-3,3},{x2,-3,3},VectorScale->{0.04,1,None},Axes->True]

splot = StreamPlot[{-3*x1+Sqrt[2]*x2,Sqrt[2]*x1-2*x2},{x1,-3,3},{x2,-3,3},VectorScale->{0.04,1,None},Axes->True]

pplot1 = ParametricPlot[{t,Sqrt[2]*t},{t,-3,3},PlotStyle->Black];
pplot2 = ParametricPlot[{-Sqrt[2]*t,t},{t,-3,3},PlotStyle->Red];

Show[vplot,pplot1,pplot2]