12.4-12.5
with(plots):with(linalg):
# Verify the vectors a,b,c are coplanar using the scalar triple product.
a:=<2,3,1>: b:=<1,-1,0>: c:=<7,3,2>:
a1 := arrow(a ,color= red):
b1 := arrow(b, color= black):
c1 := arrow(c,color= blue):
bxc:=crossprod(b,c);
dotprod(a,bxc);
display(a1,b1,c1, axes=normal,scaling=constrained);
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g1:=pointplot3d({[2,4,-3],[3,-1,1] },color=blue,symbol=circle,symbolsize=15,axes=normal):
f:=t->2+1*t;
g:=t->4-5*t;
h:=t->-3+4*t;
a:=0;
b:=2;
g2:=animate3d([f(x*t),g(x*t),h(x*t)],x=0..1,y=0..1,t=a..b,axes=normal,thickness=4,numpoints=500):display(g1,g2);
g1:=pointplot3d({[3,-1,2],[8,2,4],[-1,-2,-3]},color=red,symbol=circle,symbolsize=25,axes=normal):
a := arrow(<8,2,4>,<-5,-3,-2>):
b := arrow(<8,2,4>,<-9,-4,-7>):
display(a,b,g1, axes=normal,scaling=constrained);
#32;
a:=arrow(<2,-4,6>):
b:=arrow(<5,1,3>):
crossprod(<2,-4,6>,<5,1,3>);
vc:=arrow(crossprod(<2,-4,6>,<5,1,3>)):
display(a,b,vc, axes=normal,scaling=constrained);
g2:=implicitplot3d({-18*x+24*y+22*z=0},x=-10..10,y=-10..10,z=-10..10,axes=normal,color=blue):
display(a,b,vc,g2,scaling=constrained);