> # INTERSECTION OF TWO PLANES     Math II Fall 1996, 9/9/96
> #
> # We represent the planes parametrically and then
> # plot them on the same graph.
> #
> with(linalg):    # we want to use the crossprod function
Warning: new definition for   norm
Warning: new definition for   trace

> with(plots):     # we want to use the display command
--------------------------------------------------------------------------------
> #
> # First plane:    x-3y+2z=4
> #
> x1 := 1+3*r-2*s; y1 := -1+r; z1 := s;

                               x1 := 1 + 3 r - 2 s

                                  y1 := - 1 + r

                                     z1 := s
--------------------------------------------------------------------------------
> #
> # Second plane:    2x-y-z=3
> #
> x2 := t+u; y2 := 2*t; z2 := -3 + 2*u;

                                   x2 := t + u

                                    y2 := 2 t

                                 z2 := - 3 + 2 u
--------------------------------------------------------------------------------
> #
> # Call the plot of the first plane P1
> #
> P1 := plot3d([x1,y1,z1],r=-2..5,s=-2..5):
--------------------------------------------------------------------------------
> #
> # Call the plot of the second plane P2
> #
> P2 := plot3d([x2,y2,z2],t=-2..5,u=-2..5):
--------------------------------------------------------------------------------
> #
> # Use the display command to plot the planes on the same axes:
> #
> display({P1,P2},title=`Two planes`);
> #
> # Call the normals n1 and n2:
--------------------------------------------------------------------------------
> #
> n1 := vector([1,-3,2]);  n2:= vector([2,-1,-1]);

                               n1 := [ 1, -3, 2 ]

                               n2 := [ 2, -1, -1 ]
> #
--------------------------------------------------------------------------------
> #  Find the line of intersection of the planes:
> #
> L := crossprod(n1,n2);

                                L := [ 5, 5, 5 ]
--------------------------------------------------------------------------------
> #
--------------------------------------------------------------------------------
> #  Plot the line
> #
> Lplot := plot3d([1+5*v,-1+5*v,5*v],v=-1..1,w=0..1):
> #
> #  Stick it on the same plot as the planes:
> #
> display({P1,P2,Lplot},title=`Planes + intersection`):
--------------------------------------------------------------------------------
>