9. Extra Credit: Three points, P1, P2, and P3, with coordinates r1, r2, and r3, respectively, in the any-plane, are the vertices of an acute-angled triangle. (Here r, = (116,-, 3],), for j = 1, 2, 3.) A fourth point P with coordinates r 2 (3:, 3;) should be such that the sum of its distances dj from the points Pj, j = 1,2,3, is the smallest. Characterize P in terms of the angles between the vector pairs r r, and r r,, i, j = 1, 2, 3, i 79 j. Then show that this P indeed gives the minimal distance sum. HINT: To show that P is a minimum, show that the quadratic terms fm(A:L')2 +2 fmyAery+ fyy(Ay)2, where f = d1 + d2 + 613, can be expressed as a sum of squares