(1) Given the points P (1, 0), Q(2, 1), R(2, 3) and S = (3, x). (a) Express the vectors P Q, P R , RS and P S in Cartesian form, that is, in the form ai + bj where a and b are scalars. (b) Find the values of x for which |P R| = |P S|. (c) Put v = P Q, w = P R. Find a vector expression in terms of v and w for the vector P T where T (6, 11). (2) Given vectors u = 2i + 2j + k and v = 3i j 2k. (a) Find the unit vectors pointing in the same direction as u and v. (b) Show that the vectors u and v are linearly independent. (c) Find the vector projection of v in the direction of u. (d) Find the real number a such that the vector w = au + v is perpendicular to 2u v