xu (xx638) – Homework #4 – nevils – (77401)
1
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printout
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have
25
questions.
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before answering.
001
10.0 points
Consider the vector
→
M
= (+
a,
+
d
) = +
a
ˆ
ı
+
d
ˆ
.

b

a

c

d
d
c
a
b

b

a

c

d
d
c
a
b
F
B
A
G
C
E
D
H
x
y
Which vector is a valid representation of
→
M
?
1.
H
and
G
, but no others.
2.
G
only.
3.
H
only.
4.
B
and
E
, but no others.
5.
C
and
F
, but no others.
6.
D
,
E
,
B
, and
A
, but no others.
7.
A
only.
8.
D
only.
9.
H
,
C
,
F
, and
G
, but no others.
10.
D
and
A
, but no others.
002
(part 1 of 2) 10.0 points
Consider the two vectors
vector
M
= (
a, b
) =
a
ˆ
ı
+
b
ˆ
and
vector
N
= (
c, d
) =
c
ˆ
ı
+
d
ˆ
.
What is the value of the scalar product
vector
M
·
vector
M
?
1.
a

b
2.
2
a b
3.
a
+
b
4.
radicalbig
a
2
+
b
2
5.

2
a b
6.
a
2
+
b
2
7.
a
2

b
2
8.
a
2
+ 2
a b
+
b
2
9.
a
2

2
a b
+
b
2
003
(part 2 of 2) 10.0 points
What is the value of the scalar product
vector
M
·
vector
N
?
1.
a
2
+
b
2
+
c
2
+
d
2
2.
a d
+
b c
3.
a b
+
c d
4.
a b c d
5.
a b

c d
6.
a c
+
b d
7.
a d

b c
8.
radicalbig
a
2
+
b
2
+
radicalbig
c
2
+
d
2
9.
a c

b d
004
(part 1 of 2) 10.0 points
Consider four vectors
vector
F
1
,
vector
F
2
,
vector
F
3
, and
vector
F
4
with
magnitudes
F
1
= 36 N,
F
2
= 38 N,
F
3
= 15 N,
and
F
4
= 68 N,
θ
1
= 130
◦
,
θ
2
=

150
◦
,
θ
3
= 31
◦
, and
θ
4
=

65
◦
, measured from the
positive
x
axis with counterclockwise positive.
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xu (xx638) – Homework #4 – nevils – (77401)
2
What is the magnitude of the resultant vec
tor
vector
F
=
vector
F
1
+
vector
F
2
+
vector
F
3
+
vector
F
4
?
Answer in units of N.
005
(part 2 of 2) 10.0 points
What is the direction of this resultant vec
tor
vector
F
, within the limits of

180
◦
and 180
◦
as
measured from the positive
x
axis with coun
terclockwise positive ?
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 Spring '08
 None
 Vector Space, Dot Product, Acceleration, Work, Euclidean vector, Vertical direction

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