Chapter 13 Answers A.69 Chapter 13 Answers 13.1 Vectors in the Plane 31
Chapter 13 Answers A.69 Chapter 13 Answers 13.1 Vectors in the Plane 31. y 1. (4,9) 3. (-15, 3) 3 5. Y = 1 7. No solution 9. No solution 11. No solution 13. a = 4, b = - I 15. a = 0, b = I 17. (XI, YI) + (0,0) = (XI + 0, YI + 0) = (XI' YI) 3 x 19. [(XI' YI) + (X2, Yz)] + (x3' YJ) = (XI + X2 + X3, YI + Yz + Y3) = (XI' YI) + [(X2, Yz) + (x3, Y3)] 21. a(b(x, Y» = a(bx, by) = (abx, aby) = ab(x, y) 33. y 23. y 2 • • • • •• • • • • •• x x • •• • • • 4 • • • • • • 35. 25. (a) k(l,3) + 1(2,0) = m(1, 2) (b) k + 21 = m and 3k + 0 = 2m x (c) k = 4,1 = 1 and m = 6; i.e. 4S03 + S2 = 6S02 27. (a) d (b) e 29. (a) c + d = (6,2) -6 y 37. (a) 2 .r Q x 3 6 vAw Pl....-).R u 234 x (b) -2e+a=(-1,0) (b) v=(l,2); w=(1, -2); u=(-2,0) (c) 0 y 39. (a) y -2e+a x x (b) (0, I) A.70 Chapter 13 Answers (c) (0,5/2) 9. (d) (0, -2) x 11. w -2 (e) (I, y) (f) v=(O,y) 41. (a) Yes (c) Eliminate rand s. w (b) v = -(s/r)w (d) Solve linear equations. 13. - i + 2j + 3k 15. 7i + 2j + 3k 13.2 Vectors in Space 17. i - k 19. i - j + k 21. i + 4j, B ~ 0.24 radians east of north 1. 23.
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