1. Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics for Electrical and Computer Engineering by
Nannapaneni Narayana Rao
Edward C. Jordan Professor of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Urbana, Illinois, USA
Amrita Viswa Vidya Peetham, Coimbatore
July 10 – August 11, 2006

2. 1.1
Vector Algebra

3. (1) Vectors (A) vs. Scalars (A)
Magnitude and direction Magnitude only Ex: Velocity, Force Ex: Mass, Charge
(2) Unit Vectors have magnitude unity denoted by symbol a with subscript
Useful for expressing vectors in terms of their components.

4. (3) Dot Product is a scalar
A • B = AB cos a B
Useful for finding angle between two vectors.

5. (4) Cross Product is a vector
A B = AB sin a B
is perpendicular to both A and B.
Useful for finding unit vector perpendicular to two vectors. an

6. where
(5) Triple Cross Product
in general.

7. (6) Scalar Triple Product
is a scalar.

8. Volume of the parallelepiped

9. D1.2 A = 3a1 + 2a2 + a3
B = a1 + a2 – a3
C = a1 + 2a2 + 3a3
(a) A + B – 4C
= (3 + 1 – 4)a1 + (2 + 1 – 8)a2
+ (1 – 1 – 12)a3
= – 5a2 – 12a3

10. (b) A + 2B – C
= (3 + 2 – 1)a1 + (2 + 2 – 2)a2
+ (1 – 2 + 3)a3
= 4a1 + 2a2 – 4a3
Unit Vector =

11. (c) A • C =
= 10
(d) =
= 5a1 – 4a2 + a3

12. A • (B C) = (3a1 + 2a2 + a3) • (5a1 – 4a2 + a3) = 3 5 + 2 (–4) + 1 1
(e)
= 15 – = 8
Same as
A • (B C) = (3a1 + 2a2 + a3) • (5a1 – 4a2 + a3)
= (–4)
= 15 – 8 + 1
= 8

13. P1.5
D = B – A ( A + D = B)
E = C – B ( B + E = C)
D and E lie along a straight line.

14. What is the geometric interpretation of this result?

15. Another Example
Given
Find A.

16. To find C, use (1) or (2).