Vectors

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 08:43 PM UTC

Topics discussed:
1. Vectors
2. Dot Product
2. Cross Product
3. Lines
4. Planes

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