Please add a minimalised example (least amount of code that shows the effect) to better assess your problem. Without it, it is gonna be hard to imagine what you're doing...

Hi Simon,

I have had similar problems, but when I switched to a ViewVector notation it always seemed to work for me, unfortunately that route doesn't work here as well:

   points2=points={{-0.5408092441220346,-59.47032164154871,-33.486141445561195},{-1.6729947915403758,58.47000109642251,0.06821941845651969},{-1.1279232851470478,-12.607718410070715,-22.72024680422565},{22.74021699848095,-33.56458992369394,-25.982135247035842},{44.64374208727797,23.145194959114605,-12.259291498233077},{-24.141978569616093,-34.727887579554576,-23.475147941868702},{-47.23579711917719,20.865368869801543,-7.3461078129550135},{3.6207761893354027,-38.53425644748551,54.052848989519305},{1.6032260558335967,38.239393358088,51.948102361681556}};
   points=points[[{3,4,6,8}]];
   Graphics3D[{PointSize[Large],
   Point[points],
   Blue,Thick,
   Arrow@Tube[{points[[2]],points[[3]]}],
   Red,Thick,
   Arrow@Tube[{points[[1]],points[[4]]}],
   Opacity[.1],
   Sphere[{0,0,0},20]},
   Axes->True,
   AxesOrigin->{0,0,0},
   Boxed->False,
   BoxRatios->Automatic,
   PlotRange->All,
   ViewVector->{10000*Normalize[points[[2]]-points[[3]]],{0,0,0}},
   ViewVertical->(points[[1]]-points[[4]])
   ]
   Graphics3D[{PointSize[Large],
   Point[points2],
   Blue,Thick,
   Arrow@Tube[{points[[2]],points[[3]]}],
   Red,Thick,
   Arrow@Tube[{points[[1]],points[[4]]}],
   Opacity[.1],
   Sphere[{0,0,0},20]},
   Axes->True,
   AxesOrigin->{0,0,0},
   Boxed->False,
   BoxRatios->Automatic,
   PlotRange->All,
   ViewVector->{10000*Normalize[points[[2]]-points[[3]]],{0,0,0}},
   ViewVertical->(points[[1]]-points[[4]])
   ]

That is your code even further minimalised, and it somehow also depends on showing the other points (in some strange way)! I'm not calling this bug just yet, but it might just be one...

Hi Sander, here is an example. The red vector (between points 3 and 8) should be vertical in the final image, the blue vector (between points 4 and 6) should be in the third dimension (z-axis) in the final image. In the example below, it works as I would expect it and as I would like to use it. However, if the radius of the sphere is only 20 instead of 60 for example, then the red vector is not vertical although the settings for ViewVertical have not been changed.

Thanks for explanations or alternatives, Simon

points = {{-0.5408092441220346, -59.47032164154871, \
-33.486141445561195}, {-1.6729947915403758, 58.47000109642251, 
    0.06821941845651969}, {-1.1279232851470478, -12.607718410070715, \
-22.72024680422565}, {22.74021699848095, -33.56458992369394, \
-25.982135247035842}, {44.64374208727797, 
    23.145194959114605, -12.259291498233077}, {-24.141978569616093, \
-34.727887579554576, -23.475147941868702}, {-47.23579711917719, 
    20.865368869801543, -7.3461078129550135}, {3.6207761893354027, \
-38.53425644748551, 54.052848989519305}, {1.6032260558335967, 
    38.239393358088, 51.948102361681556}};

Show[
 ListPointPlot3D[points, 
  PlotStyle -> Directive[PointSize -> Large, Black]],
 Graphics3D[{Blue, Thick, Arrowheads -> 0.05, 
   Arrow[{points[[4]], points[[6]]}]}],
 Graphics3D[{Red, Thick, Arrowheads -> 0.05, 
   Arrow[{points[[3]], points[[8]]}]}],
 Graphics3D[{Opacity[.1], Sphere[{0, 0, 0}, 60]}],
 Axes -> True, AxesOrigin -> {0, 0, 0}, Boxed -> False, 
 BoxRatios -> Automatic, PlotRange -> All,
 ViewPoint -> 1000*Normalize[points[[4]] - points[[6]]],
 ViewVertical -> Normalize[points[[3]] - points[[8]]]
 ]