12.5: Lines in 3-Space

WINDOW:={{0,10},{0,10},{0,10}};
Origin={0,0,0};
A={1,2,3};
B={6,5,4};
V=B-A;

Manipulate[Show[Graphics3D[Arrow[{Origin,A+t  V}]],PlotRange->WINDOW,Ticks->False],{t,0,1.5,0.05}]

Manipulate[Show[
{ParametricPlot3D[A+s (B-A),{s,-0.05,t}],
Graphics3D[Arrow[{Origin,A+t  (B-A)}]]}
,PlotRange->WINDOW,Ticks->False],{t,0,1.5,0.05}]