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EXAM I
Math 51, Spring 2002.
You have 2 hours.
No notes, no books, no calculators.
YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING
TO RECEIVE CREDIT
Good luck!
Name
ID number
1.
(/20 points)
2.
(/30 points)
3.
(/20 points)
4.
(/10 points)
5.
(/20 points)
Bonus
(/10 points)
Total
(/100 points)
“On my honor, I have neither given nor
received any aid on this examination. I
have furthermore abided by all other
aspects of the honor code with respect to
this examination.”
Signature:
Circle your TA’s name:
Tarn Adams (2 and 6)
Mariel Saez (3 and 7)
Yevgeniy Kovchegov (4 and 8)
Heaseung Kwon (A02)
Alex Meadows (A03)
Circle your section meeting time:
11:00am
1:15pm
7pm
1

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*Sign up* 1. Let
-→
u
=
0
3
1
-→
v
=
3
2
2
-→
w
=
2
3
4
(a) Compute the length of each of the given vectors, and the dot product for each pair.
(b) Let
θ
-→
u ,
-→
v
be the angle formed at the origin between the vectors
-→
u
and
-→
v
. Evaluate
cos(
θ
-→
u ,
-→
v
)
2

dent.
3

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