lb  =  3;            
sp  =  1.5;

mb  =  {0, 0, lb};     
ns  =  16;                       
sv  =  
        Table[{Cos[p], Sin[p], sp}, {p, 2  Pi/ns, 2  Pi, 
            2  Pi/ns}];
                                           (* 
      Spinvektoren *)

Drehung aller Vektoren um die x-Achse um den Winkel a

a  =   .5;
dm  =  {{1, 0, 0}, {0, Cos[a], Sin[a]},  {0, -Sin[a], Cos[a]}}; 
    MatrixForm[dm]

db  =  dm . mb;; MatrixForm[db]

ds  =   Table[
          dm . {Cos[p], Sin[p], sp}, {p, 2  Pi/ns, 2  Pi, 
            2  Pi/ns}];
                                           (* 
      Spinvektoren *)

kr  =  
        ParametricPlot3D[
          Evaluate[dm . {Cos[t], Sin[t], sp}], {t, 0, 
            2  Pi}, 
AspectRatio  ->  Automatic,  
          Axes  ->  False];

ls  =  Map[Line[{#, {0, 0, 0}}] &, ds];

bv  =  Line[{db, {0, 0, 0}}];

tb  =  
        Table[Show[kr, 
            Graphics3D[{{Thickness[ .01], bv}, {RGBColor[1, 0, 0], 
                  ls[[k]]}}],  
SphericalRegion  ->  True,  BoxRatios  ->  {1, 1, 1.5},  
            Boxed  ->  
              False,  
PlotRange  ->  {{-2, 
                  2}, {-2, 2}, {-1, 
                  4}}, 
ViewPoint  ->  {5, 3.5, 
                4}, 
ViewCenter  ->  {0, 0, 0}], {k, 
            Length[ls]}];