(* This could help you *)
Export["vectors9.gif", Animate[Show[
ParametricPlot3D[{10 Cos[t], 10 Sin[t], 0}, {t, 0, 2 Pi},
PlotStyle -> {Dashed},
PlotRange -> {{-13, 13}, {-13, 13}, {-2, 2}}],
Graphics3D[{
{Ball[{10 Cos[t], 10 Sin[t], 0}, 1]},
{Line[{{0, 0, 0}, {10 Cos[t], 10 Sin[t], 0}}]},
{Red, Arrow[Tube[{{0, 0, -2}, {0, 0, 2}}]]}
}],
Boxed -> False, Axes -> False], {t, 0, 2 Pi, .01},
FrameMargins -> None]
]