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Medan Elektromagnetik chapter 1
Typology: Slides
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SUWARNOSUWARNO
School of Electrical Engineering and Informatics INSTITUT TEKNOLOGI BANDUNG 2006
Vector quantity : expressed by its magnitude and
Unit Vector
2 2 2
ax ay a z A
a^ A x y z
A x y^ z A A A
A A A
A 2 2 2 A Ax Ay Az
dot product: the product of magnitude of the two vectors and cosine of the angle between the them.
A.B=B.A =AB cos AB
Projection A on B
Length= A cos AB
2
A AB
A B
A. B cos
Anglebetween two vectors
A.A A
A.(B C) A.B A.C( )
A.B B.A( )
1 AB
(^22)
A
distributi ve
commutativ e
x y z
x y z
x y z
B B B
A A A
a a a
AxA
AxB
a xa a ;a xa a ;a xa a
0
Ax(B C) AxB AxC (distribut ive)
AxB BxA (anticommut ative)
x y z y z x z x y
x y z
x y z
x y z
22
2 a 3 a 3 a Unit vectorA a
a.Length A 2 3 3 22 x y z A
2 2 2
50 , 2^ o 22
cos^3 A
A. a cos
b.Anglebetween Adan Y axis
^
^ ^
^
145 , 1^ o 22 27
cos A B
cos
c.Anglebetween A and B
-^1 ^1 ^
3 ^