12.5: Lines in 3-Space

Needs["VisualLA`"]

WINDOW := {{0, 10}, {0, 10}, {0, 10}};
Origin = {0, 0, 0};
A = {1, 2, 3};
B = {6, 5, 4};
V = B - A;
Show[{DrawVector3D[{A}, DisplayFunction -> Identity], 
          DrawVector3D[{V}, DisplayFunction -> Identity]}, 
        PlotRange -> WINDOW, 
        DisplayFunction -> $DisplayFunction];

Table[
        Show[DrawVector3D[{A + t  V}, DisplayFunction -> Identity], 
          DisplayFunction -> $DisplayFunction, PlotRange -> WINDOW, 
          Ticks -> False], {t, 0, 1.5, 0.05}];

Table[
        Show[ParametricPlot3D[A + s AB, {s, -0.05, t}, 
            DisplayFunction -> Identity], 
          DrawVector3D[{A + t  AB}, DisplayFunction -> Identity], 
          DisplayFunction -> $DisplayFunction, PlotRange -> WINDOW, 
          Ticks -> False], {t, 0, 1.5, 0.05}];

Table[
        Show[DrawVector3D[{A}, DisplayFunction -> Identity], 
          DrawVector3D[{A +  t V}, DisplayFunction -> Identity], 
          DrawVector3D[{{A, A +  t V}}, DisplayFunction -> Identity], 
          DisplayFunction -> $DisplayFunction, PlotRange -> WINDOW, 
          Ticks -> False], {t, 0.05, 1.5, 0.05}];