Chapter 1 Euclidean spaces 12. Let u = (1, - 1, 0, 2), v = (- 2, - 1, 1, - 4), and w = (3, 2, - 1, 0). a. Find a vector a E R* such that 21 - 3v - d = W. b. Find a vector a 5 [2u - 3v + a] = 2w+ u-2d. 13. Determine whether a 1 b, 1. d = (1, 2, 3) and 6 = (-2, -4, -6). 2. a = ( - 1, 0, 1, 2) and b = ( - 3, 0, 3, 6). 3. d = (1, - 1, 1, 2) and b = (- 2, 2, 2, 3). 14. Let x, y, a, b E R with x # y. Let P(x, 2x), Q(v, 2y), P, (a, 2a), and Q,(b. that PQ IP,Q1. 15. Let P(x, 0), O(3, x2), P, (2x, 1), and 9, (6, x2). Find all possible values o