EE1259: Electromagnetic assignment 1
1
EE1259 Assignment 1
(Due on 9:30 am Thursday, September 7, 2007)
1.
Four vectors drawn from a common point are given as follows:
⎪
⎪
⎩
⎪
⎪
⎨
⎧
+
+
=
+
+
=
−
+
=
−
−
=
z
y
x
z
y
x
z
y
x
z
y
x
a
a
m
a
m
D
a
a
m
a
C
a
a
a
m
B
a
a
m
a
A
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r
r
2
2
2
2
Find the value(s) of m for each of following cases:
(a)
A
is perpendicular to
B
(b)
B
is parallel to
C
(c)
A
,
B
, and
C
lie in the same plane;
(d)
D
is perpendicular to both
A
and
B
2.
As we know from the lecture, for vector triple products, we have
( ) ( ) ( )
B
A
C
C
A
B
C
B
A
r
r
r
r
r
r
r
r
r
⋅
−
⋅
=
×
×
( ) ( ) ( )
A
C
B
B
A
C
C
B
A
r
r
r
r
r
r
r
r
r
×
⋅
=
×
⋅
=
×
⋅
Show that
()
( ) ( )
[ ] ( )
[ ]
2
C
B
A
A
C
C
B
B
A
r
r
r
r
r
r
r
r
r
⋅
×
=
×
×
×
⋅
×
3.
Given vector
z
y
x
a
a
a
A
r
r
r
r
+
−
=
2
5
, find the expression of
(a)
a unit vector
B
a
r
such that
A
a
B
r
r
//
and
(b)
a unit vector
C
a
r
in the
xy
plane
such that
A
a
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 Fall '07
 Chen
 Angular Momentum, Electromagnet, Rigid Body, vector triple products

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