Some Planes

and their equations

>	with(plots):

Warning, the name changecoords has been redefined

A plane intersecting all three axes:  

>	implicitplot3d(3*x+4*y+6*z=24,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

A plane parallel to the y-axis:  

>	implicitplot3d(3*x+6*z=24,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

A plane parallel to the x-axis:  

>	implicitplot3d(4*y+6*z=24,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

A plane parallel to the z-axis:  

>	implicitplot3d(3*x+4*y=24,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

A plane parallel to the xy-coordinate plane:  

>	implicitplot3d(z=4,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

A plane parallel to the yz-coordinate plane:  

>	implicitplot3d(x=8,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

A plane parallel to the xz-coordinate plane:  

>	implicitplot3d(y=6,x=0..10,y=0..7,z=0..5,axes=normal,labels=[x,y,z]);

Two parallel planes:         

>	plane1:=implicitplot3d(3*x+4*y+6*z=24,x=-6..10,y=-6..7,z=-6..5,axes=normal,labels=[x,y,z],scaling=constrained):

>	plane2:=implicitplot3d(3*x+4*y+6*z=-12,x=-6..10,y=-6..7,z=-6..5,axes=normal,labels=[x,y,z],scaling=constrained):

The next entry constructs a line segment perpendicular to both planes, endpoints on the planes, whose length, d, is the distance between the planes.

>	linesegment:=spacecurve([3*t,4*t,-2+6*t],t=0..36/61,color=blue,thickness=4):

>	display(plane1,plane2,linesegment);

>