Thomas Calculus 13th [Solutions]

878 Chapter 12 Vectors and the Geometry of Space
19. (a) The solid ball of radius 1 centered at the origin
(b) The exterior of the sphere of radius 1 centered at the origin
2
20. (a) The circumference and interior of the circle x
2
y 1 in the xy-plane
2
(b) The circumference and interior of the circle x
2
y 1 in the plane z 3
(c) A solid cylindrical column of radius 1 whose axis is the z-axis
21. (a) The solid enclosed between the sphere of radius 1 and radius 2 centered at the origin
(b) The solid upper hemisphere of radius 1 centered at the origin
22. (a) The line y x in the xy-plane
(b) The plane y x consisting of all points of the form ( x, x, z)
23. (a) The region on or inside the parabola
(b) The region on or to the left of the parabola
or less away from the xy-plane.
2
y x in the xy -plane and all points above this region.
2
x y in the xy -plane and all points above it that are 2 units
24. (a) All the points the lie on the plane z 1 y.
3
(b) All points that lie on the curve z y in the plane x 2.
25. (a) x 3
(b) y 1
(c) z 2
26. (a) x 3
(b) y 1
(c) z 2
27. (a) z 1
(b) x 3
(c) y 1
28. (a)
2 2
x y 4, z 0 (b)
2 2
y z 4, x 0
(c)
2 2
x z 4, y 0
29. (a)
2 2
x ( y 2) 4, z 0 (b)
2 2
( y 2) z 4, x 0 (c)
2 2
x z 4, y 2
30. (a)
2 2
( x 3) ( y 4) 1, z 1 (b)
2 2
( y 4) ( z 1) 1, x 3 (c)
2 2
( x 3) ( z 1) 1, y 4
31. (a) y 3, z 1
(b) x 1, z 1
(c) x 1, y 3
32.
2 2 2 2 2 2 2 2 2 2 2 2 2 2
x y z x ( y 2) z x y z x ( y 2) z y y 4y 4 y 1
33.
2 2 2 2 2
x y z 25, z 3 x y 16 in the plane z 3
34.
2 2 2
x y ( z 1) 4 and
2 2 2 2 2 2 2 2 2 2 2
x y ( z 1) 4 x y ( z 1) x y ( z 1) z 0, x y 3
35. 0 z 1
36. 0 x 2, 0 y 2, 0 z 2
37. z 0
38.
2 2
z 1 x y
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