Math 20C
Prof. Tesler
Midterm #1 Answer Key
October 17, 2005
Name
Answer Key
Student ID No.
Circle the section in which you are enrolled on Tuesdays:
T.A. Vladimir Pesic
C01
3–3:50 p.m.
WLH 2208
C02
4–4:50 p.m.
WLH 2208
C07
5–5:50 p.m.
Sequoyah 147
T.A. Michael Ferry
C03
5–5:50 p.m.
WLH 2208
C04
6–6:50 p.m.
WLH 2208
C05
7–7:50 p.m.
WLH 2208
C06
8–8:50 p.m.
WLH 2208
Do not open this booklet until instructed to do so.
Work alone.
Use the space provided. If necessary, write “see other side” and continue working on the
back of the same sheet.
Circle your final answers
when relevant.
You are allowed to have one doublesided sheet of notes made according to the specifica
tions explained in class. No other resources are permitted.
No calculators. You may leave answers in symbolic form, like
√
42, unless they simplify
further, like
√
9 = 3,
e
0
= 1 or cos(3
π/
4) =

√
2
/
2.
Time for midterm: 50 minutes.
1
36
/
36
2
40
/
40
3
24
/
24
Total
100
/
100
There are different versions of the test. This answer key contains detailed answers for one
version of the test, and just final answers for the other versions.
If you want to write down questions for your T.A. or you want to rework problems, please
do so on separate paper; do not write on or mark up your graded exam.
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(1) Let
~v
=
h
7
,
5
i
and
(yellow/pink)
~w
=
h
4
,

3
i
(green)
~w
=
h
6
,

3
i
(blue)
~w
=
h
8
,

3
i
. Use these values for all questions on this page.
(a) Compute 6
~v

10
~w
.
(yellow/pink)
6
h
7
,
5
i 
10
h
4
,

3
i
=
h
42
,
30
i  h
40
,

30
i
=
h
42

40
,
30

(

30)
i
=
h
2
,
60
i
(green)
6
h
7
,
5
i
10
h
6
,

3
i
=
h
42
,
30
ih
60
,

30
i
=
h
42

60
,
30

(

30)
i
=
h
18
,
60
i
(blue)
6
h
7
,
5
i
10
h
8
,

3
i
=
h
42
,
30
ih
80
,

30
i
=
h
42

80
,
30

(

30)
i
=
h
38
,
60
i
(b) Find all unit vectors perpendicular to
~v
.
The vectors perpendicular to
h
a, b
i
are all the scalar multiples of
h
b,

a
i
. In
this case,
h
5
,

7
i
is perpendicular to
h
7
,
5
i
:
h
5
,

7
i · h
7
,
5
i
= 5(7)

7(5) = 0.
The length is
 h
5
,

7
i 
=
p
5
2
+ (

7)
2
=
√
25 + 49 =
√
74.
One unit vector is
h
5
,

7
i
/
 h
5
,

7
i 
=
D
5
/
√
74
,

7
/
√
74
E
The other one is its negative
D

5
/
√
74
,
7
/
√
74
E
.
(c) Compute

10 proj
9ˆ
ı
(
~w
).
(yellow/pink)
proj
~a
(
~
b
) =
(
~a
·
~
b
)
~a

~a

2
; here,
~a
= 9ˆ
ı
,
~
b
=
~w
proj
~a
(
~
b
) =
(9ˆ
ı
·h
4
,

3
i
)9ˆ
ı
9
2
=
(9(4)+0(

3))9ˆ
ı
9
2
=
(9
2
)(4)ˆ
ı
9
2
= 4ˆ
ı
.
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 Fall '08
 Helton
 Math, Vectors, Dot Product, Parametric equation, vector parametric equation

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