1. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Chapter 12: Vectors Cartesian Space Coordinates a. Cartesian coordinates, p. 707, figure 12.1.2 Cartesian coordinates, p. 707, figure 12.1.2 b. Distance formula, equations for a sphere, p. 708 Distance formula, equations for a sphere, p. 708 c. Midpoint formula, p. 709 Midpoint formula, p. 709 Vectors a. Definition 12.3.1, p. 714, figure 12.3.1 Definition 12.3.1, p. 714, figure 12.3.1 b. Parallel vectors, p. 12.3.2 Parallel vectors, p. 12.3.2 c. Norm, properties of norm, p. 717 Norm, properties of norm, p. 717 d. Unit coordinate vectors, (12.3.5), pp. 718, 719 Unit coordinate vectors, (12.3.5), pp. 718, 719 Dot Product a. Definition 12.4.1, p. 722 Definition 12.4.1, p. 722 b. Properties of dot product, (12.4.2 – 12.4.6), pp. 722, 723 Properties of dot product, (12.4.2 – 12.4.6), pp. 722, 723 c. (12.4.7 - 9), angle between two vectors, pp. 724, 725 (12.4.7 - 9), angle between two vectors, pp. 724, 725 d. (12.4.13), direction angles, direction cosines, p. 728, figure 12.4.7 (12.4.13), direction angles, direction cosines, p. 728, figure 12.4.7 e. Triangle inequality, p. 729 Triangle inequality, p. 729 Cross Product a. Definition 12.5.1, p. 733 Definition 12.5.1, p. 733 b. Properties of cross product, (12.5.2 – 4), pp. 733, 734 Properties of cross product, (12.5.2 – 4), pp. 733, 734 c. Triple scalar product, (12.5.5-6), p. 734, figure 12.5.5 Triple scalar product, (12.5.5-6), p. 734, figure 12.5.5 d. Theorem 12.5.8’, p. 736 Theorem 12.5.8’, p. 736 Lines a. Vector equation of a line, p. 741, figures 12.6.1-2 Vector equation of a line, p. 741, figures 12.6.1-2 b. Direction vector, direction numbers, p. 742, figure 12.6.4 Direction vector, direction numbers, p. 742, figure 12.6.4 c. Scalar equations, symmetric equations, (12.6.4-5), pp. 743, 744 Scalar equations, symmetric equations, (12.6.4-5), pp. 743, 744 d. Distance point to a line, (12.6.7), p. 748, figure 12.6.10 Distance point to a line, (12.6.7), p. 748, figure 12.6.10 Planes a. Scalar equation, (12.7.1), p. 750, figure 12.7.1 Scalar equation, (12.7.1), p. 750, figure 12.7.1 b. Vector equation, (12.7.2-3), p. 752, figure 12.7.3 Vector equation, (12.7.2-3), p. 752, figure 12.7.3 c. Distance from a point to a plane, (12.7.7), p. 757, figure 12.7.7 Distance from a point to a plane, (12.7.7), p. 757, figure 12.7.7

2. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cartesian Space Coordinates Cartesian coordinates, p. 707, figure 12.1.2

3. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cartesian Space Coordinates Distance formula, equations for a sphere, p. 708

4. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cartesian Space Coordinates Midpoint formula, p. 709

5. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vectors Definition 12.3.1, p 714, figure 12.3.1

6. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vectors Parallel vectors, p. 12.3.2

7. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vectors Norm, properties of norm, p. 717

8. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Vectors Unit coordinate vectors, (12.3.5), pp. 718, 719

9. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Dot Product Definition 12.4.1, p.722

10. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Dot Product Properties of dot product, (12.4.2 – 12.4.6), pp. 722. 723

11. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Dot Product (12.4.7-9), angle between two vectors, pp. 724, 725

12. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Dot Product (12.4.13), directional angles, direction cosines, p. 728, figure 12.4.7

13. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Dot Product Triangle inequality, p. 729

14. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cross Product Definition 12.5.1, p.733

15. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cross Product Properties of cross product, (12.5.2 – 4), pp. 733, 734

16. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cross Product Triple scalar product, (12.5.5-6), p. 734, figure 12.5.5

17. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Cross Product Theorem 12.5.8’, p. 736

18. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Lines Vector equation of a line, p. 741, figures 12.6.1-2

19. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Lines Direction vector, direction numbers, p. 742, figure 12.6.4

20. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Lines Scalar equations, symmetric equations, (12.6.4-5), pp. 743, 744

21. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Lines Distance point to a line, (12.6.7), p. 748, figure 12.6.10

22. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Planes Scalar equation, (12.7.1), p. 750, figure 12.7.1

23. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Planes Vector equation, (12.7.2-3), p. 752, figure 12.7.3

24. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Planes Distance from a point to a plane, (12.7.7), p. 757, figure 12.7.7