Chapter One: Vector Analysis The use of vectors and vector analysis ...

Electromagnetic Theorem
(Dr. Omed Ghareb Abdullah) University of Sulaimani –College of Science – Physics Department
2 1
2
(b). Q ( R P)
2 3 1 2
(3 0) 1
(2 2) 2
(0 6) 6 4 12
14
2 0 1
(c).
sin
QR
Q R
aˆ
x
Q R
Q R 2
Q R
2
25 4 16
45
aˆ
y
aˆ
z
1
2
3 1
,
Q
aˆ
( 1
6) aˆ
(4 2) aˆ
( 6
2) 5aˆ
2aˆ
x
4 1
4 3
and
y
z
R 4 9 1
14
x
y
4aˆ
z
sin
QR
3
45
14
0.596
(d).
aˆ
x
aˆ
y
aˆ
z
P ( Q R)
2 0 1
aˆ
(0 2) aˆ
( 5
8) aˆ
(4 0) 2aˆ
3aˆ
4aˆ
5 2 4
x
y
z
x
y
z
(e).
aˆ
QR
Q R
Q R
5aˆ
x
2 aˆ
y
3 14
4 aˆ
z
(f). The scalar and vector component P along Q can be calculated as follows:
The scalar component of P along Q is equal to:
P Q
P
ˆ
Q
P cos
P aQ
Q
2 aˆ
ˆ 2 ˆ
x
a
y
a
z 4 2 2
P aˆ
(2
aˆ
ˆ
Q
x
a
z
)
3 3 3
The vector component of P along Q is given by:
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