12.5: Examples

Lines in 3-Space using a point and direction vector

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}]

Line Segment between two points

r[t_]={2,-1,4}+t{2,7,-3};

Show[
{
ParametricPlot3D[{2+2 t,-1+7 t,4-3 t},{t,-5,0},PlotStyle->{Red},PlotRange->{{-10,10},{-10,30},{-10,10}},AxesLabel->{x,y,z}],
ParametricPlot3D[{2+2 t,-1+7 t,4-3 t},{t,1,5},PlotStyle->{Red},PlotRange->{{-10,10},{-10,30},{-10,10}},AxesLabel->{x,y,z}],
ParametricPlot3D[{2+2 t,-1+7 t,4-3 t},{t,0,1},PlotStyle->{Thick,Blue},PlotRange->{{-10,10},{-10,30},{-10,10}},AxesLabel->{x,y,z}]
}
]

Intersection of planes

P1[x_,y_]=1-x;
P2[x_,y_]=((3-y)/2);
P3[x_,y_]=((1-y-x)/(-2));
Show[
{
Plot3D[P1[x,y],{x,-3,3},{y,-3,3}],
Plot3D[P2[x,y],{x,-3,3},{y,-3,3}],
Plot3D[P3[x,y],{x,-3,3},{y,-3,3}]
}
]