Problem 1E: Explain how to plot the point (3, 2, 1) in 3. Problem 2E: What is the y-coordinate of all points in the xz-plane? Problem 3E: Describe the plane x = 4. Problem 4E Problem 5E: Let u = 3, 5, 7 and v = 6, 5, 1. Evaluate u + v and 3u v. Problem 6E: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)? Problem 7E: Which point is farther from the origin, (3, 1, 2) or (0, 0, 4)? Problem 8E: Express the vector from P(1, 4, 6) to Q(1, 3, 6) as a position vector in terms of i, j, and k. Problem 9E: Points in 3 Find the coordinates of the vertices A, B, and C of the following rectangular boxes. 9. Problem 10E: Points in 3 Find the coordinates of the vertices A, B, and C of the following rectangular boxes. 10. Problem 11E: Points in 3 Find the coordinates of the vertices A, B, and C of the following rectangular boxes. 11. Problem 12E: Points in 3 Find the coordinates of the vertices A, B, and C of the following rectangular boxes. 12.... Problem 13E: Plotting points in 3 For each point P(x, y, z) given below, let A(x, y, 0), B(x, 0, z), and C(0, y,... Problem 14E: Plotting points in 3 For each point P(x, y, z) given below, let A(x, y, 0), B(x, 0, z), and C(0, y,... Problem 15E: Sketching planes Sketch the following planes in the window [0, 5] [0, 5] [0, 5]. 15. x = 2 Problem 16E: Sketching planes Sketch the following planes in the window [0, 5] [0, 5] [0, 5]. 16. z = 3 Problem 17E: Sketching planes Sketch the following planes in the window [0, 5] [0, 5] [0, 5]. 17. y = 2 Problem 18E: Sketching planes Sketch the following planes in the window [0, 5] [0, 5] [0, 5]. 18. z = y Problem 19E: Sketching planes Sketch the following planes in the window [0, 5] [0, 5] [0, 5]. 19. The plane... Problem 20E: Sketching planes Sketch the following planes in the window [0, 5] [0, 5] [0, 5]. 20. The plane... Problem 21E: Planes Sketch the plane parallel to the xy-plane through (2, 4, 2) and find its equation. Problem 22E Problem 23E: Spheres and balls Find an equation or inequality that describes the following objects. 23. A sphere... Problem 24E: Spheres and balls Find an equation or inequality that describes the following objects. 24. A sphere... Problem 25E: Spheres and balls Find an equation or inequality that describes the following objects. 25. A ball... Problem 26E: Spheres and balls Find an equation or inequality that describes the following objects. 26. A ball... Problem 27E: Midpoints and spheres Find an equation of the sphere passing through P(1, 0, 5) and Q(2, 3, 9) with... Problem 28E: Midpoints and spheres Find an equation of the sphere passing through P(4, 2, 3) and Q(0, 2, 7) with... Problem 29E: Identifying sets Give a geometric description of the following sets of points. 29. (x 1)2 + y2 + z2... Problem 30E: Identifying sets Give a geometric description of the following sets of points. 30. (x + 1)2 + y2 +... Problem 31E: Identifying sets Give a geometric description of the following sets of points. 31. x2 + y2 + z2 2y ... Problem 32E: Identifying sets Give a geometric description of the following sets of points. 32. x2 + y2 + z2 6x... Problem 33E: Identifying sets Give a geometric description of the following sets of points. 33. x2 + y2 14y + z2... Problem 34E Problem 35E: Identifying sets Give a geometric description of the following sets of points. 35. x2 + y2 + z2 8x ... Problem 36E: Identifying sets Give a geometric description of the following sets of points. 36. x2 + y2 + z2 8x... Problem 37E: Identifying sets Give a geometric description of the following sets of points. 37. x2 2x + y2 + 6y... Problem 38E: Identifying sets Give a geometric description of the following sets of points. 38. x2 4x + y2 + 6y... Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E: Unit vectors and magnitude Consider the following points P and Q. a. Find PQ and state your answer... Problem 46E: Unit vectors and magnitude Consider the following points P and Q. a. Find PQ and state your answer... Problem 47E: Unit vectors and magnitude Consider the following points P and Q. a. Find PQ and state your answer... Problem 48E: Unit vectors and magnitude Consider the following points P and Q. a. Find PQ and state your answer... Problem 49E Problem 50E: Unit vectors and magnitude Consider the following points P and Q. a. Find PQ and state your answer... Problem 51E: Flight in crosswinds A model airplane is flying horizontally due north at 20 mi/hr when it... Problem 52E: Another crosswind flight A model airplane is flying horizontally due east at 10 mi/hr when it... Problem 53E: Crosswinds A small plane is flying horizontally due east in calm air at 250 mi/hr when it is hit by... Problem 54E Problem 55E Problem 56E: Maintaining equilibrium An object is acted upon by the forces F1 = 10, 6, 3 and F2 = 0, 4, 9. Find... Problem 57E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 58E: Sets of points Describe with a sketch the sets of points (x, y, z) satisfying the following... Problem 59E: Sets of points Describe with a sketch the sets of points (x, y, z) satisfying the following... Problem 60E: Sets of points Describe with a sketch the sets of points (x, y, z) satisfying the following... Problem 61E: Sets of points 61. Give a geometric description of the set of points (x, y, z) satisfying the pair... Problem 62E: Sets of points 62. Give a geometric description of the set of points (x, y, z) satisfying the pair... Problem 63E: Sets of points 63. Give a geometric description of the set of points (x, y, z) that lie on the... Problem 64E: Sets of points 64. Give a geometric description of the set of points (x, y, z) that lie on the... Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E: Parallel vectors of varying lengths Find vectors parallel to v of the given length. 69. v=PQ with... Problem 70E: Parallel vectors of varying lengths Find vectors parallel to v of the given length. 70. v=PQ with... Problem 71E: Collinear points Determine whether the points P, Q, and R are collinear (lie on a line) by comparing... Problem 72E: Collinear points Determine the values of x and y such that the points (1, 2, 3), (4, 7, 1), and (x,... Problem 73E: Lengths of the diagonals of a box What is the longest diagonal of a rectangular 2 ft 3 ft 4 ft box? Problem 74E Problem 75E: Three-cable load A 500-kg load hangs from three cables of equal length that are anchored at the... Problem 76E: Four-cable load A 500-lb load hangs from four cables of equal length that are anchored at the points... Problem 77E: Possible parallelograms The points O(0, 0, 0), P(1, 4, 6), and Q(2, 4, 3) lie at three vertices of a... Problem 78E Problem 79E: Midpoint formula Prove that the midpoint of the line segment joining P(x1, y1, z1) and Q(x2, y2, z2)... Problem 80E: Equation of a sphere For constants a, b, c, and d, show that the equation x2+y2+z22ax2by2cz=d... Problem 81E Problem 82E: Medians of a trianglewith coordinates In contrast to the proof in Exercise 81, we now use... Problem 83E: The amazing quadrilateral propertycoordinate free The points P, Q, R, and S, joined by the vectors... Problem 84E format_list_bulleted
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage