The medians of a triangle meet at a point P (the centroid by Problem 30 of Section 5.6) that is two-thirds of the way from a vertex to the midpoint of the opposite edge. Show that p is the head of the position vector (a + b + c)/3, where a, b, and c are the position vector of the vertices, and use this to find p if the vertices are (2, 6, 5), (4, -1, 2), and (6, 1, 2).