F[{x_, y_, z_}] = {-y^10, Cos[x*y*z] + Sin[Sin[z]], Cos[x] - x};
Manipulate[ 
Show[Graphics3D[{Blue, Opacity[0.5], Sphere[{0,0,0},a]},Boxed->False],
 VectorPlot3D[F[{x, y, z}], {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, VectorPoints->5,
  VectorColorFunction -> Hue, VectorScale -> 0.17,Boxed->False]],{a,0.3,1.3}]