Problem 1 Projection vector. Let P = (9, 2, 1), Q = (5,5, 2), and R = (7, -2,4). Let a = PQ and b = PR. (i) Find a , the projection vector of a along b. (ii) Do P, Q, and R lie on the same line? Explain using the projection you found in part (i).Problem 2 Intersection of a line and a plane. Let / be the line whose parametric equation is defined by r(t) = (1 + t, 1 - 2t, 3 + 5t). Let " be the plane 2x - y + 32 - 48 = 0. (i) Find the point of intersection Q of the line I and the plane . (ii) Find an equation of the plane . that passes through the point Q and is orthogonal to I.Prnbleln 3 Plane determined by a triangle. Lat P = {3:311}: Q = {2: _1:]r and R = [1r _3:-1i' [1} Dean PIER term a. right triangle?ll Find the area, the triangle PEER. {ii} Find the equation of the plane determined by the paints P1 [:2 and R