Laboratory Session 2 command lines.



1. 


restart:with(plots):with(linalg):


 a:=[-1,1,1];b:=[-7/13,21/13,37/13];

 p:=[12,-3,-2];q:=[4,-12,3];

 r1:=t->evalm(a+t*p):r1(t);

 r2:=s->evalm(b+s*q):r2(s);

 solution:=solve({r1(t)[1]=r2(s)[1],r1(t)[2]=r2(s)[2]},{t,s});

 assign(solution);

 t, s; 

 r1(t);r2(s);

 t:='t';s:='s';

 l1:=spacecurve(r1(t),t=-1..1,color=red,axes=frame,thickness=3):

 l2:=spacecurve(r2(s),s=-1..1,color=blue,thickness=3):

 display(l1,l2);

 uu:=evalm(crossprod(p,q));

 u:=evalm(uu/norm(uu,2));


-------------------------------------------------------------------------


plane1:=implicitplot3d(dotprod([x,y,z]-r1(0),u)=0,x=-10..10,y=-10..10, z=-10..10,style=patchnogrid):

plane2:=implicitplot3d(dotprod([x,y,z]-r2(0),u)=0,x=-10..10,y=-10..10, z=-10..10,style=patchnogrid):

display(l1,l2,plane1,plane2);

v:=r1(0)-r2(0);

distance:=abs(dotprod(v,u));

l3:=spacecurve(evalm(r2(0)+w*u),w=0..distance,thickness=3,color=green):

display(l1,l2,plane1,plane2,l3);




2. 


 restart:with(plots):with(linalg):

 r1:=t->cos(t):r2:=t->sin(t):r3:=t->t:

 r:=t->[r1(t),r2(t),r3(t)];

 dr:=[D(r1),D(r2),D(r3)];

 tangent:=s->evalm(r(a)-s*dr(a)):tangent(s);

 a:=1;

 tangent(s);

 c1:=spacecurve(r(t),t=0..10,color=black,thickness=3):

 c2:=spacecurve(tangent(s),s=-1..1,color=blue,thickness=3):

 display(c1,c2,orientation=[0,20]);

 c3:=plot3d(1,theta=0..2*Pi,z=-1..10,coords=cylindrical,style=patchnogrid):

 display(c1,c2,c3);





3.


 restart:with(plots):

 cone:=plot3d(z,theta=0..2*Pi,z=-3..3,coords=cylindrical,orientation = [140,70], style=patchnogrid):

 p1:=plot3d(2,x=-3..3,y=-3..3):

 p2:=plot3d(.6*x+1,x=-3..3,y=-3..3):

 p3:=plot3d(x+1,x=-3..3,y=-3..3):

 p4:=implicitplot3d(x=1,x=-3..3,y=-3..3,z=-3..3):

 p5:=implicitplot3d(x=0,x=-3..3,y=-3..3,z=-3..3):

 display(cone,p1,scaling=constrained);

 display(cone,p2,scaling=constrained);

 display(cone,p3,scaling=constrained);

 display(cone,p4,scaling=constrained);

 display(cone,p5,scaling=constrained);