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

Appendix I Answers to Odd-Numbered Exercises A119
35. z − sx 2 1d 2 1 sy 2 3d 2 z
Circular paraboloid with
vertex s1, 3, 0d and axis the
vertical line x − 1, y − 3
sx 2 2d 2
37. 2 y2 sz 2 1d2
1 − 1
5 5 5
Hyperboloid of one sheet with
center s2, 0, 1d and axis the
horizontal line x − 2, z − 1
x (1, 3, 0)
z
y
Exercises
1. (a) sx 1 1d 2 1 sy 2 2d 2 1 sz 2 1d 2 − 69
(b) sy 2 2d 2 1 sz 2 1d 2 − 68, x − 0
(c) Center s4, 21, 23d, radius 5
3. u v − 3s2; | u 3 v | − 3s2; out of the page
5. 22, 24 7. (a) 2 (b) 22 (c) 22 (d) 0
9. cos 21 ( 1 3 ) < 71° 11. (a) k4, 23, 4 l (b) s41y2
13. 166 N, 114 N
15. x − 4 2 3t, y − 21 1 2t, z − 2 1 3t
17. x − 22 1 2t, y − 2 2 t, z − 4 1 5t
19. 24x 1 3y 1 z − 214 21. (1, 4, 4) 23. Skew
25. x 1 y 1 z − 4 27. 22ys26
29. Plane 31. Cone
z
z
y
0
39.
4
41.
2
x
y
x
x
33. Hyperboloid of two sheets 35. Ellipsoid
y
z 0
z 0
z
z
(0, 1, 2)
_4
_4
43. z
0
y
4 4
0
x
z=2
_4
_2
_2 0 2
y
0
2 x
_2
x
(0, 2, 0)
y
(1, 1, 0)
x
(0, 1, -2)
(0, 2, 0)
y
37. 4x 2 1 y 2 1 z 2 − 16
x
0
z=œ„„„„„ ≈+¥
y
45. x − y 2 1 z 2 47. 24x − y 2 1 z 2 , paraboloid
x 2
49. (a)
s6378.137d 1 y 2
2 s6378.137d 1 z 2
2 s6356.523d − 1 2
(b) Circle (c) Ellipse
53.
2
z 1
0
1
0
y
1
1
0
x
1
Problems PLUs • page 844
1. ss3 2 3 2d m
3. (a) sx 1 1dys22cd − sy 2 cdysc 2 2 1d − sz 2 cdysc 2 1 1d
(b) x 2 1 y 2 − t 2 1 1, z − t (c) 4y3
5. 20
Chapter 13
Exercises 13.1 • page 853
1. s21, 3d 3. i 1 j 1 k 5. k21, y2, 0 l
7.
y
π
9.
z
Chapter 12 Review • page 842
True-False Quiz
1. False 3. False 5. True 7. True 9. True
11. True 13. True 15. False 17. False
19. False 21. True
1
x
(0, 2, 0)
x y
3c3 Ans 10.1.5
09.21.04
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