%  illustrates cross (vector) product 
%  and the volume of parallelepiped

P = [0, 1, 2];
Q = [2,4,5];
R =[-1,0,1];
S = [6,-1,4];

a = Q - P;   % vectors a,b,c
b = R - P;
c = S - P;

 arrow3([0,0,0], [1,0,0],'yellow');
 arrow3([0,0,0], [0,1,0],'yellow');
 arrow3([0,0,0], [0,0,1],'magenta');    % this plots the i,j,k, vectors

arrow3(P, Q,'red');
arrow3(P, R,'green');
arrow3(P, S,'blue');    % this plots the vectors
     
axb = cross(a,b);    % cross-product
arrow3(P, P + axb, 'black');

 plot3([-2,-2,7], [-2,7,-2], [7,-2,-2],'*w')   % this sets the window of specified size
 
 Qp = S + a;
 lineOM(S,Qp);   % this adds remaining lines to the ppiped 
 lineOM(Q,Qp);
 
 T = Q + b; 
 lineOM(Q, T);
 lineOM(R, T);
 
 Rp = R + c;
 lineOM(R, Rp); 
 lineOM(S,Rp);
 
 Tp = T+c;
 lineOM(T,Tp);
 lineOM(Qp, Tp);
 lineOM(Rp, Tp);