cooper (mlc4285) – HW 01 – florin – (55245)
1
This
printout
should
have
20
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0points
Which of the following are vectors?
List all
that apply, separated by commas.
A
4
.
5
B
0
C
(
0
.
7
,
0
.
7
,
0
.
5
)
D
(
0
,
2
.
3
,
−
1
)
E
−
1
×
10
6
F
6
· (
14
,
0
,
−
22
)
Correct answer: C, D, F.
Explanation:
Options
A
,
B
, and
E
are scalar quanti
ties, so those choices are incorrect.
Options
C
and
D
are clearly vectors, so they are cor
rect choices.
The only option that might be
somewhat tricky is
F
, which gives a vector be
ing multiplied by a scalar. But the product of
such scalar multiplication is a new vector, so
this choice is also correct.
002(part1of3)10.0points
The figure shows the three dimensional vector
vector
d
.
What are the components of the
vector
d
1.
(−
6
,
−
3
,
2
)
m
2.
(−
6
,
−
3
,
−
2
)
m
3.
(−
6
,
3
,
2
)
m
correct
4.
(−
6
,
3
,
−
2
)
m
5.
(
6
,
3
,
2
)
m
Explanation:
Since the tail of the vector is at the origin,
the components of
vector
d
can be read off from the
figure being careful to get the sign correct.
The xcomponent is
−
6 m; the ycomponent
is +2 m; and the zcomponent is +3 m.
003(part2of3)10.0points
If the tail of vector
vector
d
is moved to location
(
3
.
2
,
3
.
2
,
3
.
5
)
m, where would the tip of the
vector be located?
1.
(−
2
.
8
,
6
.
2
,
5
.
5
)
m
correct
2.
(
9
.
2
,
−
0
.
2
,
−
1
.
5
)
m
3.
(
3
.
2
,
3
.
2
,
3
.
5
)
m
4.
(−
6
,
3
,
2
)
m
5.
(−
6
,
−
3
,
2
)
m
Explanation:
Shifting
the
tail
of
the
vector
to
(
3
.
2
,
3
.
2
,
3
.
5
)
m means each component of the
tip of the vector will be changed by the same
amount as each component of the tail was
changed.
Thus, the tip will be at
(−
6 +
3
.
2
,
3 + 3
.
2
,
2 + 3
.
5
)
m =
(−
2
.
8
,
6
.
2
,
5
.
5
)
m.
004(part3of3)10.0points
What is the length of the vector
vectore
=
−
vector
d
? Give
your answer in units of meters.
Correct answer: 7 m.
Explanation:
We use the Pythagorean theorem:

vectore

=
radicalBig
e
2
x
+
e
2
y
+
e
2
z
=
radicalBig
(6 m)
2
+ (
−
3 m)
2
+ (
−
2 m)
2
=
√
49 m
2
= 7
.
0 m
.