Unformatted text preview: at is contained in the ﬁrst octant.
3 23–34  Describe in words the region of
equation or inequality. 23. y 24. x 27. 0 z 29. x 2 y2 z2 2 y 33. x 2
■ 2 35–38 25 2z 3 z z2 ■ z2 2 32. x 2
34. xyz 9
■  z 1 y2 x2 30. 1
31. x 6 0 28. y 3 10 26. y 4 25. x represented by the ■ ■ ■ ■ ■ y2 1 0
■ ■ ■ ■ Write inequalities to describe the region. 35. The halfspace consisting of all points to the left of the xzplane
36. The solid rectangular box in the ﬁrst octant bounded by the planes x 1, y 2, and z 3 37. The region consisting of all points between (but not on) the
13. Find an equation of the sphere that passes through the point 4, 3, 1 and has center 3, 8, 1 . spheres of radius r and R centered at the origin, where r 38. The solid upper hemisphere of the sphere of radius 2 centered at the origin 14. Find an equation of the sphere that passes through the origin and whose center is 1, 2, 3 . R ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 5E13(pp 828837) 834 ❙❙❙❙ 1/18/06 11:10 AM Page 834 CHAPTER 13 VECTORS AND THE GEOMETRY OF SPACE 39. The ﬁgure shows a line L 1 in space and a second line L 2 , which is the projection of L 1 on the xyplane. (In other words,
z L¡ the points on L 2 are directly beneath, or above, the points
on L 1.)
(a) Find the coordinates of the point P on the line L 1.
(b) Locate on the diagram the points A, B, and C, where
the line L1 intersects the xyplane, the yzplane, and the
xzplane, respectively.
40. Consider the points P such that the distance from P to P A 1, 5, 3 is twice the distance from P to B 6, 2, 2 . Show
that the set of all such points is a sphere, and ﬁnd its center and
radius. 1
0
1 41. Find an equation of the set of all points equidistant from the L™ 1 points A
y x 1, 5, 3 and B 6, 2, 42. Find the volume of the solid that lies inside both of the spheres x2 y2 z2 4x
x2 and  13.2 2 . Describe the set. y2 2y
z2 4z 5 0 4 Vectors D
B u v
C
A F IGURE 1 Equivalent vectors The term vector is used by scientists to indicate a quantity (such as displacement or velocity...
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 Fall '09
 hamrick
 Linear Algebra, Vectors, Vector Space, Dot Product, (pp 828837)

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