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MATH 32A EXAM I
OCTOBER 19, 2009
LAST NAME
FIRST NAME
ID NO.
•
WRITE CLEARLY AND LEGIBLY.
•
TO RECEIVE CREDIT, YOU MUST CIRCLE YOUR ANSWERS
.
PLEASE DO NOT WRITE BELOW THIS LINE
SCORES
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5(
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TOTAL
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PROBLEM 1
Let
v
=
h
1
,
1
,
1
i
. Write the vector
w
=
h
3
,
2
,
1
i
as a sum
w
=
w

+
w
⊥
where
w

is parallel to
v
and
w
⊥
is perpendicular to
v
.
Solution:
We have
w

=
±
v
·
w
v
·
v
²
v
=
³
h
1
,
1
,
1
i·h
1
,
2
,
3
i
h
1
,
1
,
1
1
,
1
,
1
i
´
h
1
,
1
,
1
i
=
h
2
,
2
,
2
i
and
w
⊥
=
w
−
w

=
h
3
,
2
,
1
i−h
2
,
2
,
2
i
=
h
1
,
−
0
,
−
1
i
The decomposition with respect to
v
is
w
=
h
3
,
2
,
1
i
=
h
2
,
2
,
2
i
+
h
1
,
−
0
,
−
1
i
3
PROBLEM 2
Two vectors
v
and
w
(based at the origin) of length 8 lie in the plane
2
x
+3
y
−
4
z
=0
The angle between
v
and
w
is
θ
=
π/
6. With this information you can
determine the cross product
v
×
w
up to a sign. Find a vector
u
such that
v
×
w
=
±
u
.
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This note was uploaded on 10/26/2011 for the course MATH 32A taught by Professor Gangliu during the Spring '08 term at UCLA.
 Spring '08
 GANGliu
 Math

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