Thomas Calculus 13th [Solutions]

CHAPTER 12
VECTORS AND THE GEOMETRY OF
SPACE
12.1 THREE-DIMENSIONAL COORDINATE SYSTEMS
1. The line through the point (2, 3, 0) parallel to the z-axis
2. The line though the point ( 1, 0, 0) parallel to the y-axis
3. The x-axis
4. The line through the point (1, 0, 0) parallel to the z-axis
5. The circle
2 2
x y 4 in the xy-plane
6. The circle
2 2
x y 4 in the plane z 2
7. The circle
2 2
x z 4 in the xz-plane
8. The circle
2 2
y z 1 in the yz-plane
9. The circle
2 2
y z 1 in the yz-plane
10. The circle
2 2
x z 9 in the plane y 4
11. The circle
2 2
x y 16 in the xy-plane
12. The circle
2 2
x z 3 in the xz-plane
13. The ellipse formed by the intersection of the cylinder
2 2
x y 4 and the plane z y.
14. The circle formed by the intersection of the sphere
2 2 2
x y z 4 and the plane y x.
15. The parabola
16. The parabola
2
y x in the xy-plane.
2
z y in the plane x 1.
17. (a) The first quadrant of the xy -plane
(b) The fourth quadrant of the xy-plane
18. (a) The slab bounded by the planes x 0 and x 1
(b) The square column bounded by the planes x 0, x 1, y 0, y 1
(c) The unit cube in the first octant having one vertex at the origin
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