James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

Appendix I Answers to Odd-Numbered Exercises A117
37. 2177.39 i 1 211.41 j, 177.39 i 1 138.59 j;
275.97 N, 225.11 N
39. (a) At an angle of 43.48 from the bank, toward upstream
(b) 20.2 min
41. 6si 1 4 jdys17 43. 0
45. (a), (b)
y
0
sa
b
tb
a
47. A sphere with radius 1, centered at sx 0, y 0, z 0d
c
x
(d) s − 9 7, t − 11 7
Exercises 12.3 • page 812
1. (b), (c), (d) are meaningful 3. 23.6 5. 19 7. 1
9. 14s3 11. u v − 1 2 , u w − 21 2
15. cos 21S 1
s5
D < 63° 17. cos 21 (2 5 6) < 146°
19. cos 21S 7
s130
D < 52° 21. 48°, 75°, 57°
23. (a) Orthogonal (b) Neither
(c) Parallel (d) Orthogonal
25. Yes 27. si 2 j 2 kdys3 for s2i 1 j 1 kdys3g
29. 45° 31. 0° at s0, 0d, 8.1° at s1, 1d
33. 2 3 , 1 3 , 2 3 ; 48°, 71°, 48°
35. 1ys14 , 22ys14 , 23ys14 ; 748, 1228, 1438
37. 1ys3, 1ys3, 1ys3; 55°, 55°, 55° 39. 4, k2 20
13 , 48
13 l
41. 1 9 , k 4 81 , 7 81 , 2 4 81 l 43. 27ys19 , 2 21
19 i 1 21
19 j 2 7 19 k
47. k0, 0, 22s10 l or any vector of the form
ks, t, 3s 2 2s10l, s, t [ R
49. 144 J 51. 2400 coss40°d < 1839 ft@lb
53. 13 5 55. (1ys3) cos21 < 55°
Exercises 12.4 • page 821
1. 15 i 2 10 j 2 3 k 3. 14 i 1 4 j 1 2 k
5. 2 3 2 i 1 7 4 j 1 2 3 k 7. s1 2 td i 1 st 3 2 t 2 d k
9. 0 11. i 1 j 1 k
13. (a) Scalar (b) Meaningless (c) Vector
(d) Meaningless (e) Meaningless (f) Scalar
15. 96s3; into the page 17. k27, 10, 8 l, k 7, 210, 28 l
19. K2 1
3s3 , 2 1
3s3 , 5
L, K 1
3s3 3s3 , 1
L
3s3 , 2 5
3s3
27. 20 29. (a) k0, 18, 29 l (b) 9 2 s5
31. (a) k13, 214, 5 l (b) 1 2 s390
33. 9 35. 16 39. 10.8 sin 80° < 10.6 N ? m
41. <417 N 43. 60°
45. (b) s97y3 53. (a) No (b) No (c) Yes
Exercises 12.5 • page 831
1. (a) True (b) False (c) True (d) False
(e) False (f) True (g) False (h) True (i) True
(j) False (k) True
3. r − s2 i 1 2.4 j 1 3.5 kd 1 ts3 i 1 2 j 2 kd;
x − 2 1 3t, y − 2.4 1 2t, z − 3.5 2 t
5. r − si 1 6kd 1 tsi 1 3j 1 kd;
x − 1 1 t, y − 3t, z − 6 1 t
7. x − 2 1 2t, y − 1 1 1 2 t, z − 23 2 4t;
sx 2 2dy2 − 2y 2 2 − sz 1 3dys24d
9. x − 28 1 11t, y − 1 2 3t, z − 4; x 1 8 − y 2 1
11 23 , z − 4
11. x − 26 1 2t, y − 2 1 3t, z − 3 1 t;
sx 1 6dy2 − sy 2 2dy3 − z 2 3
13. Yes
15. (a) sx 2 1dys21d − s y 1 5dy2 − sz 2 6dys23d
(b) s21, 21, 0d, s2 3 2 , 0, 23 2d, s0, 23, 3d
17. rstd − s6i 2 j 1 9kd 1 tsi 1 7j 2 9kd, 0 < t < 1
19. Skew 21. s4, 21, 25d 23. x 2 2y 1 5z − 0
25. x 1 4y 1 z − 4 27. 5x 2 y 2 z − 7
29. 6x 1 6y 1 6z − 11 31. x 1 y 1 z − 2
33. 5x 2 3y 2 8z − 29 35. 8x 1 y 2 2z − 31
37. x 2 2y 2 z − 23 39. 3x 2 8y 2 z − 238
41.
z
43.
z
x
(5, 0, 0)
0
(0, 0, 10)
(0, 2, 0)
y
(0, _2, 0)
x
3
”0, 0, ’
2
0
(1, 0, 0)
45. s22, 6, 3d 47. ( 2 5 , 4, 0) 49. 1, 0, 21
51. Perpendicular 53. Neither, cos D 21S2
1 < 114.1°
s6
55. Parallel
21S 57. (a) x − 1, y − 2t, z − t (b) cos
3s3D 5 < 15.88
59. x − 1, y 2 2 − 2z
61. x 1 2y 1 z − 5
63. sxyad 1 syybd 1 szycd − 1
65. x − 3t, y − 1 2 t, z − 2 2 2t
67. P 2 and P 3 are parallel, P 1 and P 4 are identical
69. s61y14 71. 18 7 73. 5ys2s14d
77. 1ys6 79. 13ys69
81. (a) x − 325 1 440t, y − 810 2 135t, z − 561 1 38t,
0 < t < 1 (b) No
Exercises 12.6 • page 839
1. (a) Parabola
(b) Parabolic cylinder with rulings parallel to the z-axis
(c) Parabolic cylinder with rulings parallel to the x-axis
y
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