MATH 230 HOMEWORK 2  DUE IN CLASS ON 9/9/09
PAUL SIEGEL, INSTRUCTOR
Instructions:
Solve all problems completely. The use of calculators or computer
aids is permitted but not required; full credit will be given only if all work is shown.
You are encouraged to work with other students, but the solutions that you hand
in must be written by you in your own words and they should be a re±ection of
your own thinking. If you do choose to work with other students, please hand in a
list of all group members with your solutions.
Problem 1.
Section 13.2.
(a) Suppose the points
A
,
B
, and
C
in
R
3
are the vertices of a triangle. What is
±±!
AB
+
±±!
BC
+
±!
CA
?
(b) Let
r
0
=
h±
3
;
2
;
±
2
i
. Describe the set of all vectors
r
with the property that
j
r
±
r
0
j ²
4.
(c) Let
r
1
=
h±
1
;
2
i
and let
r
2
=
h
1
;
0
i
. Describe the set of all vectors
r
with the
property that
j
r
±
r
1
j
+
j
r
±
r
2
j
= 4.
(d) (Section 13.3) Let
a
=
h
a
1
;a
2
;a
3
i
, and
b
=
h
b
1
;b
2
;b
3
i
. Show that the set of all
vectors
r
which satisfy (
r
±
a
)
³
(
r
±
b
) = 0 is a sphere and ²nd its radius.
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 '08
 WEINERMICHAELDA

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