Pictures For Section 12.3 Number 36

Surface and Plane Intersections

The point (red cross) and the line tangent to the curve at the point (in green) have been added to each picture in this worksheet.

>	with(plots):

>	curve1:=spacecurve([t,Pi/3,cos(2*t-Pi/3)],t=0..2,color=blue,thickness=4):

>	surface1:=plot3d(cos(2*x-y),x=0..2,y=0..2,axes=boxed,labels=[x,y,z]):

>	plane1:=implicitplot3d(y=Pi/3,x=0..2,y=0..2,z=-1..2,axes=boxed):

>	point1:=pointplot3d([Pi/4,Pi/3,sqrt(3)/2],color=red,symbol=cross,symbolsize=50):

>	tangentline1:=spacecurve([Pi/4+t,Pi/3,sqrt(3)/2-t*sqrt(2)],t=-Pi/4..2-Pi/4,color=green,thickness=4):

>	display(surface1,plane1,curve1,point1,tangentline1);

>	curve2:=spacecurve([Pi/4,t,cos(Pi/2-t)],t=0..2,color=blue,thickness=4):

>	plane2:=implicitplot3d(x=Pi/4,x=0..2,y=0..2,z=-1..1.4,axes=boxed):

>	tangentline2:=spacecurve([Pi/4,Pi/3+t,sqrt(3)/2+t/2],t=-Pi/3..2-Pi/3,color=green,thickness=4):

>	display(surface1,plane2,curve2,point1,tangentline2);

>	curve3:=spacecurve([t,4*t/3,cos(2*t/3)],t=0..1.5,color=blue,thickness=4):

>	plane3:=implicitplot3d(y=4*x/3,x=0..2,y=0..2,z=-1..1.2,axes=boxed):

>	tangentline3:=spacecurve([Pi/4+t,Pi/3+4*t/3,sqrt(3)/2-t/3],t=-Pi/4..3/2-Pi/4,color=green,thickness=4):

>	display(surface1,plane3,curve3,point1,tangentline3);

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