Chapter 13

# The yz plane the x axis the z axis y2 0 1 33 x 2 z2 9

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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 half-space consisting of all points to the left of the xz-plane 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 ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 5E-13(pp 828-837) 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 xy-plane. (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 xy-plane, the yz-plane, and the xz-plane, 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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