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

A116 Appendix I Answers to Odd-Numbered Exercises
Chapter 12
Exercises 12.1 • page 796
1. s4, 0, 23d 3. C; A
5. A line parallel to the y-axis and 4 units to the right of it; a vertical
plane parallel to the yz-plane and 4 units in front of it.
z
y
x=4
0 4
x
4
0
y
45. 14x 2 6y 2 10z − 9, a plane perpendicular to AB
47. 2s3 2 3
Exercises 12.2 • page 805
1. (a) Scalar (b) Vector (c) Vector (d) Scalar
3. AB l − DC l , DA l − CB l , DE l − EB l , EA l − CE l
5. (a)
(b) u
u+v v
w
u+w
u
(c)
w
v
v+w
(d)
u
u-v
_v
7. A vertical plane that z
intersects the xy-plane in
the line y − 2 2 x, z − 0
x
y=2-x
(e)
v
u
w
v+u+w
(f)
_w
u
u-w-v
_v
0
y=2-x, z=0
7. c − 1 2 a 1 1 2 b, d − 1 2 b 2 1 2 a
9. (a) | PQ | − 6, | QR | − 2s10, | RP |
x
2
− 6; isosceles triangle
11. (a) No (b) Yes
13. sx 1 3d 2 1 sy 2 2d 2 1 sz 2 5d 2 − 16;
sy 2 2d 2 1 sz 2 5d 2 − 7, x − 0 (a circle)
15. sx 2 3d 2 1 sy 2 8d 2 1 sz 2 1d 2 − 30
17. s1, 2, 24d, 6 19. s2, 0, 26d, 9ys2
21. (b) 5 2 , 1 2 s94 , 1 2 s85
23. (a) sx 2 2d 2 1 sy 1 3d 2 1 sz 2 6d 2 − 36
(b) sx 2 2d 2 1 sy 1 3d 2 1 sz 2 6d 2 − 4
(c) sx 2 2d 2 1 sy 1 3d 2 1 sz 2 6d 2 − 9
25. A plane parallel to the yz-plane and 5 units in front of it
27. A half-space consisting of all points to the left of the
plane y − 8
29. All points on or between the horizontal planes z − 0 and z − 6
31. All points on a circle with radius 2 with center on the z-axis
that is contained in the plane z − 21
33. All point on a sphere with radius 2 and center s0, 0, 0d
35. All points on or between spheres with radii 1 and s5 and
centers s0, 0, 0d
37. All points on or inside a circular cylinder of radius 3 with axis
the y-axis
39. 0 , x , 5 41. r 2 , x 2 1 y 2 1 z 2 , R 2
43. (a) (2, 1, 4) (b) L¡ z
C
P
2
y
9. a − k 3, 1 l 11. a − k21, 4 l
A(_2, 1)
y
0
B(1, 2)
a
13. a − k2, 0, 22 l 15. k5, 2 l
x
z
0
a
17. k3, 8, 1 l
x
z
k3, 0, 1l
A(0, 3, 1)
B(2, 3, _1)
k3, 8, 1l
k0, 8, 0l
y
x
a
y
0
k_1, 4l
y
0
B(2, 3)
19. k6, 3 l, k6, 14 l, 5, 13
21. 6i 2 3j 2 2 k, 20 i 2 12 j, s29 , 7
23. K 3
s10 s10L , 2 1 25. 8 9 i 2 1 9 j 1 4 9
y
x
A(3, _1)
k6, _2l
k5, 2l
k 27. 608
x
x
0
A
L
y
29. k2, 2s3l 31. < 45.96 ftys, <38.57 ftys
33. 100s7 < 264.6 N, <139.1°
B
35. s493 < 22.2 miyh, N8°W
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