Problem 1. Consider the points P = (1, 2, 0), Q = (0, 1, 2), and R = (2, 0, 1). a. Draw a picture which shows that PQ = 00 - OP. and calculate the distance from P to Q. b. Let A be an arbitrary point in 3-dimensional space. Draw a picture which shows that A lies on the line segment joining P and Q if and only if OA = OP + +PQ. for some value of t. c. If M is the midpoint of the line segment PQ, give values of a and b such that OM = GOP + boQ. Check your answer by verifying that the distances from P to M and Q to M are equal. d. The centroid of the triangle APQR can be defined as the unique point C such that OC = -OP + OQ + OR. Find the Cartesian coordinates of the centroid of APQR, and show that it lies on the median MR. e. In general, if T is any three-dimensional triangle, show that the three medians of T are concurrent (i.e. they intersect at a common point). Hint: The point where the medians intersect is the centroid