Plotting a triangle formed by 3d vectors in maple

[kyva1929]

Suppose that I have three 3d vectors, pq, pr, and v, where v is the cross product of pq and pr.

I want to fill the triangle formed by these three vectors, as shown in the picture. But I'm having difficulties finding the right command doing so, I've tried the polygonplot and apparently it supports only input of vertexes in Cartesian point format.

http://math.rutgers.edu/courses/251/Lab_Backgrounds/Images/map1_image12.gif

thank you so much!

 

[LCKurtz]

Two non-parallel vectors and their cross-product would be three sides determining a 3-d parallelepiped, or maybe a tetrahedron, but not a triangle.

One way to do a triangle and shade it in Maple would be to actually plot a portion of the plane in whatever color. Something like this for a triangle formed by two vectors:

restart:with(VectorCalculus):BasisFormat(false):
u:=<3|-3|-1>;v:=<-2|-3|2>;
plane:=s*u+t*v;
plot3d(plane,s=0..1-t,t=0..1,color=green,axes=boxed,style=patchcontour);

 

[kyva1929]

I misread the instruction given, however, I still have troubles with the orientation of the triangle.

I plot a triangle with P, Q, R being the vertexes, and I expected that two sides of the triangle should be parallel to the vectors PQ and PR. But it doesn't seem to be the case (I used P as the origin for the vectors).

I've checked the data multiple times and haven't yet been able to find the reason why it is so. Please take a look at that, thank you!

Here is the data:p = [10, 15, 10]
q = [15, 14, 16]
r = [15, 12, 9]

Thank you so much for the help!

 

[LCKurtz]

I hadn't seen the polygonplot command before. Try this:

restart:with(VectorCalculus):BasisFormat(false):with(plots):
>p := <10| 15| 10>:
> q := <15| 14| 16>:
> r := <15| 12| 9>:
>
> t1:=spacecurve(t*p+(1-t)*q,t=0..1,color=blue,thickness=2):
> t2:=spacecurve(t*p+(1-t)*r,t=0..1,color=blue,thickness=2):
> t3:=spacecurve(t*r+(1-t)*q,t=0..1,color=blue,thickness=2):
> triangle:=polygonplot3d([p,q,r]):
> display({t1,t2,t3,triangle},axes=normal,labels=[x,y,z]);

 

[kyva1929]

I hadn't seen the polygonplot command before. Try this:

restart:with(VectorCalculus):BasisFormat(false):with(plots):
>p := <10| 15| 10>:
> q := <15| 14| 16>:
> r := <15| 12| 9>:
>
> t1:=spacecurve(t*p+(1-t)*q,t=0..1,color=blue,thickness=2):
> t2:=spacecurve(t*p+(1-t)*r,t=0..1,color=blue,thickness=2):
> t3:=spacecurve(t*r+(1-t)*q,t=0..1,color=blue,thickness=2):
> triangle:=polygonplot3d([p,q,r]):
> display({t1,t2,t3,triangle},axes=normal,labels=[x,y,z]);

Thank you! It works with defining P Q and R in

>p := <10| 15| 10>:
> q := <15| 14| 16>:
> r := <15| 12| 9>:

this way, but I have no idea why it wouldn't work in the form [x,y,z] ?

 

[LCKurtz]

I dunno. Maple's distinction between lists, vectors, and matrices is confusing to me too.