ECE 329
Homework 1
Due: Jan 22, 2008, 5PM
1. Let
A
= 3ˆ
x
+ ˆ
y

2ˆ
z,
B
= ˆ
x
+ ˆ
y

ˆ
z,
C
= ˆ
x

2ˆ
y
+ 3ˆ
z,
where
ˆ
x
,
ˆ
y
, and
ˆ
z
denote an orthogonal set of unit vectors directed along the principal axes of a
righthanded Cartesian coordinate system (denoted as
a
x
,
a
y
, and
a
z
in the text). Calculate:
a) The vector magnitude

A
+
B

4
C

.
b) The unit vector
ˆ
u
along the vector
A
+ 2
B

C
.
c) The dot product
A
·
B
.
d) The cross product
B
×
C
.
e) The scalar triple product
A
·
(
B
×
C
)
.
f) If vectors
A
,
B
,
C
above are measured in units of meters, what would be the unit of the triple
product
A
·
(
B
×
C
)
and what would be the geometrical interpretation of

A
·
(
B
×
C
)

?
g) If vector
C
has velocity units (m/s),
B
has magnetic flux density units (T), and
A
has distance
units (m), what would be the unit of the scalar triple product
A
·
(
B
×
C
)
?
What physical
parameter would the unit describe? (Hint: you can think in terms of a Lorentz force analogy.)
2. Charges
Q
1
= 8
π
o
C and
Q
2
=

Q
1
/
2
are located at points
P
1
ans
P
2
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 Spring '08
 FRANKE
 Vectors, Dot Product, Force, Electromagnet, Differential length vector

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