In continuation to my previous question, I have (a slightly modified) function
f[x_,y_,z_,a_,b_,c_]:=x^2 a b + xy b c+ yz c a + z^3 abc , and I want to randomly choose values of x,y,z,a,b,c (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1 and a+b+c=1) and plot f[x,y,z,a,b,c] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a,b,c)$.

I am editing this question with additional constraints given by four inequalities $|x\pm y| \le |1\pm z|$ which simplify to $z \ge x+y-1; ~z\le -x+y+1;~z\le x-y+1;~z \ge -x-y-1.$

How can one take into account these?

In continuation to my previous question, I have (a slightly modified) function
f[x_,y_,z_,a_,b_,c_]:=x^2 a b + xy b c+ yz c a + z^3 abc , and I want to randomly choose values of x,y,z,a,b,c (with constraints that all $x,y,z$, and $a,b,c$ are positive, and Sqrt[x^2+y^2+z^2]<=1 and a+b+c=1) and plot f[x,y,z,a,b,c] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a,b,c)$.

I am editing this question with additional constraints given by four inequalities $|x\pm y| \le |1\pm z|$ which simplify to $z \ge x+y-1; ~z\le -x+y+1;~z\le x-y+1;~z \ge -x-y-1.$

How can one take into account these?

EDIT: It was "all ... and $a,b,c$ are positive" and not just $a$.