 Given z>0, n vectors p_1,\cdots,p_n on the plane, and a vector b\in\mathbb{R^n, compute a unit vector x and a permutation \pi:
<clarity>  Given z>0, n vectors p_1,\cdots,p_n on the plane, and a vector b\in\mathbb{R^n, compute a unit vector x and a permutation \pi:
 Given z>0, n vectors p_1,\cdots,p_n ^n, compute a unit vector x and a permutation \pi: