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
More example on Chapter One
Example(10):
Given vectors
(a). A B
(b). 3 A
B
A aˆ
3aˆ
and B 5aˆ
x
z
x
2aˆ
y
6aˆ
z
, then determine the following:
(c). the component of A along aˆ
y
(d). the unit vector parallel to 3A
B
Solution:
(a). A
B ( aˆ
3aˆ
) (5aˆ
2aˆ
6aˆ
) 6aˆ
2 aˆ
3 aˆ
A
B
36 4 9 7unit
x
z
x
y
z
x
y
z
(b). 3A
B
(3aˆ
9aˆ
) (5aˆ
2aˆ
6aˆ
) 2aˆ
2aˆ
15aˆ
x
z
x
y
z
x
y
z
(c). the scalar component of
A along aˆ
is given by: A Aaˆ
( aˆ
3aˆ
) aˆ
0
y
y
y
x
z
y
(d). 3A
B
(3aˆ
9aˆ
) (5aˆ
2aˆ
6aˆ
) 8aˆ
2aˆ
3aˆ
, then the unit vector
x
z
x
y
z
x
y
z
parallel to this vector is calculated as:
3A
B
a ˆ3 AB
3A
B
8aˆ
x
2 aˆ
y
3aˆ
64 4 9
z
8aˆ
x
2 aˆ
y
77
6 aˆ
z
Example(11):
Given points P( 1, 3,5) , Q(2,4,6)
and R(0,3,8)
, then find the following:
(a). the position vectors of P and R
(b). the distance vector r
QP
(c). the distance between Q and R
Solution:
62