Zu Aufgabe 2

Ausgangsposition

{1,1,1}

Drehung um die zx-Achse um 60  Grad

d[a_]:={{Cos[a],-Sin[a]},{Sin[a],Cos[a]}};
u=Append[d[60 Degree].{1,1},1]

%//N

Drehung um die x-Achse um 45  Grad

v=Prepend[d[45 Degree].{u[[2]],u[[3]]},u[[1]]]//Simplify

%//N

Drehung um die z-Achse um -60  Grad

w=Append[d[-60 Degree].{v[[1]],v[[2]]},v[[3]]]

%//N

o={0,0,0};

Zeichnung

Options[ParametricPlot3D]

p=ParametricPlot3D[Sqrt[2]{Cos[fi],Sin[fi],z},{fi,0,Pi},{z,0,2},Boxed->False,Axes->False,Shading->False,ViewPoint->{-1.630, -4.260, 1.110}];

Show[p,Graphics3D[{PointSize[0.02],Point[{1,1,1}],Point[u],Point[v],Point[w],Line[{o,{1,1,1}}],Line[{o,u}],Line[{o,v}],Line[{o,w}],Line[{{-1,0,0},{1,0,0}}],Line[{{0,-1,0},{0,1,0}}],Line[{{0,0,-1},{0,0,1}}]}],Boxed->False,ViewPoint->{-1.630, -4.260, 1.110}];

Show[p,Graphics3D[{PointSize[0.02],Point[{1,1,1}],Point[u],Point[v],Point[w],Line[{o,{1,1,1}}],Line[{o,u}],Line[{o,v}],Line[{o,w}],Line[{{-1,0,0},{1,0,0}}],Line[{{0,-1,0},{0,1,0}}],Line[{{0,0,-1},{0,0,1}}]}],Boxed->False,ViewPoint->{1.630, 4.260, 1.110}];

p=ParametricPlot3D[Sqrt[2]{Cos[fi],Sin[fi],z},{fi,0,Pi},{z,0,2},Boxed->False,Axes->False,Shading->False,ViewPoint->{-1.630, -4.260, 1.110}];