plotSurfaces = ContourPlot3D[{x^2 + y^2 == 1, x+y+z== 0}, {x, -1.5,1.5}, {y, -1.5,1.5}, {z, -2,2}, ContourStyle -> Opacity[1], AxesLabel ->{x,y,z}]

plotCurve = ParametricPlot3D[{Cos[t], Sin[t], -Cos[t]-Sin[t]}, {t, 0, 4Pi}, AxesLabel ->{x,y,z}, PlotStyle -> Red]

Show[plotSurfaces, plotCurve]

p0 = {1/Sqrt[2], 1/Sqrt[2], -Sqrt[2]};
nCylinder = {(Sqrt[2]), (Sqrt[2]), 0};
nPlane ={1,1,1};
vCurve ={ -1/Sqrt[2], 1/Sqrt[2], 0};
plotVectors = Graphics3D[{Arrow[Tube[{p0, p0+vCurve}, .03]],Thick,Orange, Arrow[{p0, p0+nCylinder}],Blue,Arrow[{p0, p0+nPlane}] }];
Show[plotSurfaces, plotCurve, plotVectors, BoxRatios -> Automatic, PlotRange ->{{-1.5, 2.1},{-1.5, 2.1}, {-2,2}}]