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Elements of ElectromagneticsFourth Edition

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2

Vector Algebra

4

Elements of Electromagnetics Fourth Edition Sadiku 5Copyright © 2007 Oxford University Press

Figure 1.1 (a) Unit vectors ax, ay, and az, (b) components of A along ax, ay, and az.

Elements of Electromagnetics Fourth Edition Sadiku 6Copyright © 2007 Oxford University Press

Figure 1.2 Vector addition C A B: (a) parallelogram rule, (b) head-to-tail rule.

Elements of Electromagnetics Fourth Edition Sadiku 7Copyright © 2007 Oxford University Press

Figure 1.3 Vector subtraction D A B: (a) parallelogram rule, (b) head-to-tail rule.

Elements of Electromagnetics Fourth Edition Sadiku 8Copyright © 2007 Oxford University Press

Figure 1.4 Illustration of position vector rP 3ax 4ay 5az.

Elements of Electromagnetics Fourth Edition Sadiku 9Copyright © 2007 Oxford University Press

Figure 1.5 Distance vector rPQ.

Elements of Electromagnetics Fourth Edition Sadiku 10Copyright © 2007 Oxford University Press

Figure 1.6 For Example 1.3.

Elements of Electromagnetics Fourth Edition Sadiku 11Copyright © 2007 Oxford University Press

Figure 1.7 The cross product of A and B is a vector with magnitude equal to the area of the parallelogram and direction, as indicated.

Elements of Electromagnetics Fourth Edition Sadiku 12Copyright © 2007 Oxford University Press

Figure 1.8 Direction of A B and an using (a) the right-hand rule and (b) the right-handed-screw rule.

Elements of Electromagnetics Fourth Edition Sadiku 13Copyright © 2007 Oxford University Press

Figure 1.9 Cross product using cyclic permutation (a) Moving clockwise leads to positive results. (b) Moving counterclockwise leads to negative results.

Elements of Electromagnetics Fourth Edition Sadiku 14Copyright © 2007 Oxford University Press

Figure 1.10 Components of A along B: (a) scalar component AB, (b) vector component AB .

Elements of Electromagnetics Fourth Edition Sadiku 15Copyright © 2007 Oxford University Press

Figure 1.11 For Example 1.6.

Elements of Electromagnetics Fourth Edition Sadiku 16Copyright © 2007 Oxford University Press

Figure 1.12 For Example 1.7.

Elements of Electromagnetics Fourth Edition Sadiku 17Copyright © 2007 Oxford University Press

Figure 1.13 For Review Question 1.3.

Elements of Electromagnetics Fourth Edition Sadiku 18Copyright © 2007 Oxford University Press

Figure 1.14 For Problem 1.20.