>	with(plots): with(VectorCalculus):

 

>	r:=(u,v)->[u*sin(v),u*cos(2*v),2*v];

 

(1)

 

>	sp:=plot3d(r(u,v),u=0..3,v=0..Pi,axes=boxed,labels=[x,y,z]): sp;

 

>	diff(r(u,v),u); diff(r(u,v),v);

 

 

	(2)

 

>	CrossProduct(Vector([sin(v),cos(2*v),0]), Vector([u*cos(v), -2*u*sin(2*v),2]));

 

(3)

 

>

h:=0.3:x0:=1:y0:=1: dMat := array(1..2): dMat[1] := display( spacecurve({[x0+t,y0,0]},t=0..h,thickness=5,color=blue), spacecurve({[x0,y0+t,0]},t=0..h,thickness=5,color=green), spacecurve({[x0+t,y0+h,0]},t=0..h,thickness=5,color=red), spacecurve({[x0+h,y0+t,0]},t=0..h,thickness=5,color=red), spacecurve({[3,t,0]},t=0..Pi,thickness=5,color=yellow), spacecurve({[0,t,0]},t=0..Pi,thickness=5,color=yellow), spacecurve({[t,0,0]},t=0..3,thickness=5,color=yellow), spacecurve({[t,Pi,0]},t=0..3,thickness=5,color=yellow), orientation=[-90,0],axes=normal,labels=[u,v,""] ): dMat[2] := display( sp, spacecurve(r(x0+t,y0),t=0..h,thickness=5,color=blue), spacecurve(r(x0,y0+t),t=0..h,thickness=5,color=green), spacecurve(r(x0+t,y0+h),t=0..h,thickness=5,color=red), spacecurve(r(x0+h,y0+t),t=0..h,thickness=5,color=red), orientation=[40,75],axes=normal,labels=[x,y,z] ): display(dMat);

 

>