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 Cartesian coordinates, p. 707, figure 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 , p. 714, figure Definition , p. 714, figure b. Parallel vectors, p Parallel vectors, p 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 , p. 722 Definition , p. 722 b. Properties of dot product, ( – ), pp. 722, 723 Properties of dot product, ( – ), pp. 722, 723 c. ( ), angle between two vectors, pp. 724, 725 ( ), angle between two vectors, pp. 724, 725 d. ( ), direction angles, direction cosines, p. 728, figure ( ), direction angles, direction cosines, p. 728, figure e. Triangle inequality, p. 729 Triangle inequality, p. 729 Cross Product a. Definition , p. 733 Definition , p. 733 b. Properties of cross product, ( – 4), pp. 733, 734 Properties of cross product, ( – 4), pp. 733, 734 c. Triple scalar product, ( ), p. 734, figure Triple scalar product, ( ), p. 734, figure d. Theorem ’, p. 736 Theorem ’, p. 736 Lines a. Vector equation of a line, p. 741, figures Vector equation of a line, p. 741, figures b. Direction vector, direction numbers, p. 742, figure Direction vector, direction numbers, p. 742, figure c. Scalar equations, symmetric equations, ( ), pp. 743, 744 Scalar equations, symmetric equations, ( ), pp. 743, 744 d. Distance point to a line, (12.6.7), p. 748, figure Distance point to a line, (12.6.7), p. 748, figure Planes a. Scalar equation, (12.7.1), p. 750, figure Scalar equation, (12.7.1), p. 750, figure b. Vector equation, ( ), p. 752, figure Vector equation, ( ), p. 752, figure c. Distance from a point to a plane, (12.7.7), p. 757, figure Distance from a point to a plane, (12.7.7), p. 757, figure

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

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

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

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

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

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

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

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

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, ( – ), pp

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

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

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

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

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, ( – 4), pp. 733, 734

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

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

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

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

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

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

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

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

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