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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online