@Lali_miani  I've already wrote  "To simplify the answer the numerical values of the system parameters should be specified" 

For example:

indets(Sys) minus {x, y, z};

L :=  %=~ [1, 2, 3, 4, 5, 6, 7, 8, 9];

solve(eval(Sys, L), {x, y, z});

evalf([%]);

@tomleslie  When I simplified the specification of the system, I accidentally deleted this factor. I've fixed it.

@one man   The package  geom3d  does not contain any direct commands for plotting and finding the parameters of a circle in 3D, so this work is very useful. The value of the work will be higher if it to be written as a procedure for any three points in 3D (of course, if these points do not lie on a straight line).

@Spinosaurus  I do not see any problems. You yourself put tickmarks on  y-axis  which you need for a corresponding plot:

P:=plot([sin(x)/4, cos(x)+2.4, 1.2], x=0..2*Pi, -1.2..3.6, color=[red,blue,black], tickmarks = [piticks, [seq(0.25*i = i*10^(`-5`), i = -1 .. 1), seq(0.5*i+2.4 = 0.5*i, i = -2 .. 2)]], axes=box):
T:=plots:-textplot([[4.2,0.2,y=sin(x)/10^`5`], [4,2.5,y=cos(x)]], font=[times,roman,14]):
plots:-display(P, T, scaling=constrained);

@asa12   Add the option  linestyle = solid  to the code.

@asa12  I repeat again:  you must first click by the mouse on the plot, and press "play " (a triangle symbol) on the animation panel.

@asa12  In my code  sols  is  a list not a vector. So try first convert your  sols[11]  into list:

convert(sols[11], list);

@asa12   My code works in Maple 12. You should just click by the mouse on the plot, and press "play " on the animation panel.
n is the number of vertices in the broken line (nops(sols)= 9), and 5 is the number of frames to display each segment. If the number of frames to increase, it will be more smooth animation.

@acer  Yes you are right,  assuming exp(2)-1>0  can be omitted. I wrote it by an analogy with sqrt(x^2) assuming x>0;

@Carl Love  You changed your style - instead of a single line of a code you write three lines.

Matrix(2,3, (i,j)->`if`(i=1,`Matrix `||j, LinearAlgebra[RandomMatrix](2)));

@RafaeldeGomes

Example:

L1:=seq(LinearAlgebra[RandomMatrix](2), i=1..5);
L2:=seq(LinearAlgebra[RandomMatrix](2), i=1..5);
L3:=seq(LinearAlgebra[RandomMatrix](2), i=1..5);
for k from 1 to 5 do
L1[k], L2[k], L3[k]
od;

@MDD  If you need to repeat a similar plotting several times, a special procedure is required for this. The planes forming facets of your polyhedral cone should be the parameters of this procedure.

I also got this message after about 15 - 20 minutes  as I posted the answer to Brian's question. Then I accidentally discovered that Brian's question mysteriously turned into a post. I would like to get an explanation of who did so.

Unfortunately I do not remember where I wrote about this formula, so I wrote again this simple procedure. The procedure returns the oriented area of a non-self-intersecting polygon:

Shoelace:=proc(L::list)
local n;
n:=nops(L); 
(1/2)*add(L[i, 1]*L[i+1, 2]-L[i, 2]*L[i+1, 1], i = 1 .. n-1);
end proc: 

Example of use:

L:=[[3, -1], [-2, 2], [5, 6], [2, 3/2], [3, -1]]:
Shoelace(L);
plots[display](plottools[polygon](L, color=yellow));

In this post  Shoelace  procedure was generalized  (Area  procedure) for a region in the plane bounded by a non-self-intersecting piecewise smooth curve.

@MDD   A, B, C  are the points of intersections of the plane  x+y+z = 1  with the original planes (I put these points on the plot). The faces of the obtained solid angle is easy to paint in any color using  color option in plots:-polygonplot3d  command. Edges also can be painted, if you use  plottools[line]  command:

restart; 
S := {-x+2*y, -x-y+3*z, 3*x-2*y-z, x+y+z = 1}: 
A, B, C:=map2(eval, [x,y,z], solve~([seq(S minus {S[i]}, i = 1 .. 3)]))[ ]; 
OO := [0, 0, 0]:
Points:=plots:-textplot3d([[A[],"A",align=below],[B[],"B", align=above],[C[],"C",align=below]], font=[times,roman,16]):  
plots:-display(Points,plots:-polygonplot3d([[OO, A, B], [OO, A, C], [OO, B, C]], color=[red,green,blue], axes = normal, labels = [x, y, z], labelfont = [times, roman, 16], orientation=[70,65,0]));

Solid_angle1.mw