Problem 1E: Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive... Problem 2E: Sketch the points (0, 5, 2), (4, 0, 1), (2, 4, 6), and (1, 1, 2) on a single set of coordinate axes. Problem 3E: Which of the points A(4, 0, 1), B(3, 1, 5), and C(2, 4, 6) is closest to the yz-plane? Which point... Problem 4E Problem 6E: (a) What does the equation x = 4 represent in 2? What does it represent in 3? Illustrate with... Problem 5E: Describe and sketch the surface in 3 represented by the equation x + y = 2. Problem 7E Problem 9E: Determine whether the points lie on a straight line. (a) A(2, 4, 2), B(3, 7, 2), C(1, 3, 3) (b)... Problem 8E: Find the distance from (4, 2, 6) to each of the following. (a) The xy-plane (b) The yz-plane (c) The... Problem 10E: Find an equation of the sphere with center (2, 6, 4) and radius 5. Describe its intersection with... Problem 11E: Find an equation of the sphere that passes through the point (4, 3, 1) and has center (3, 8, 1). Problem 12E: Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3). Problem 13E: Show that the equation represents a sphere, and find its center and radius. 17. x2 + y2 + z2 2x -... Problem 14E Problem 15E Problem 16E Problem 17E: (a) Prove that the midpoint of the line segment from P1(x1, y1, z1) to P2(x2, y2, z2) is... Problem 18E: Find an equation of a sphere if one of its diameters has end-points (2, 1, 4) and (4, 3, 10). Problem 19E: Find equations of the spheres with center (2, 3, 6) that touch (a) the xy-plane, (b) the yz-plane,... Problem 20E: Find an equation of the largest sphere with center (5, 4, 9) that is contained in the first octant. Problem 21E: Describe in words the region of 3 represented by the equation(s) or inequality. 25. x = 5 Problem 22E: Describe in words the region of 3 represented by the equation(s) or inequality. 26. y = 2 Problem 23E: Describe in words the region of 3 represented by the equation(s) or inequality. 27. y 8 Problem 24E: Describe in words the region of 3 represented by the equations or inequalities. x3 Problem 25E: Describe in words the region of 3 represented by the equation(s) or inequality. 29. 0 z 6 Problem 26E: Describe in words the region of 3 represented by the equations or inequalities. Z2 = 1 Problem 27E: Describe in words the region of 3 represented by the equations or inequalities. x2+y2+z23 Problem 28E: Describe in words the region of 3 represented by the equation(s) or inequality. 36. x = z Problem 29E: Describe in words the region of 3 represented by the equation(s) or inequality. 37. x2 + z2 9 Problem 30E: Describe in words the region of 3 represented by the equation(s) or inequality. 38. x2 + y2 + z2 2z Problem 31E: Write inequalities to describe the region. 39. The region between the yz-plane and the vertical... Problem 32E: Write inequalities to describe the region. 40. The solid cylinder that lies on or below the plane z... Problem 33E: Write inequalities to describe the region. 41. The region consisting of all points between (but not... Problem 34E: Write inequalities to describe the region. 42. The solid upper hemisphere of the sphere of radius 2... Problem 35E: Find an equation of the set of all points equidistant from the points A(1, 5, 3) and B(6, 2, 2).... Problem 36E: Find the volume of the solid that lies inside both of the spheres x2 + y2 + z2 + 4x 2y + 4z + 5 = 0... Problem 37E: Find the distance between the spheres x2 + y2 + z2 = 4 and x2 + y2 + z2 = 4x + 4y + 4z 11. Problem 38E: Describe and sketch a solid with the following properties. When illuminated by rays parallel to the... format_list_bulleted