pasha (sep635) – HW#11 – Antoniewicz – (56445)
1
This printout should have 36 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001 (part 1 of 5) 2.0 points
Consider vectors
~
A
and
~
B
such that
~
A
=
h
200
,

200
,

300
i
and
~
B
=
h
300
,
500
,
300
i
.
±ind
~
A
+
~
B
.
1.
h
100
,
300
,
0
i
correct
2.
h
100
,
200
,

100
i
3.
h
200
,
100
,

200
i
4.
h
300
,
0
,
100
i
5.
h
200
,
300
,
200
i
Explanation:
To add vectors, we add respective compo
nents:
A
x
+
B
x
=200+(

300) =

100
,
A
y
+
B
y
=

200 + 500 = 300
,
and
A
z
+
B
z
=

300 + 300 = 0
,
so
~
A
+
~
B
=
h
A
x
+
B
x
,A
y
+
B
y
z
+
B
z
i
=
h
100
,
300
,
0
i
.
002 (part 2 of 5) 2.0 points
±ind
±
±
±
~
A
+
~
B
±
±
±
.
Correct answer: 316
.
228.
Explanation:
The magnitude oF
~
A
+
~
B
is
±
±
±
~
A
+
~
B
±
±
±
=
q
(
A
x
+
B
x
)
2
+(
A
y
+
B
y
)
2
A
z
+
B
z
)
2
=
q
(

100)
2
+(300)
2
+(0)
2
=316
.
228
.
003 (part 3 of 5) 2.0 points
±ind
±
±
±
~
A
±
±
±
.
Correct answer: 412
.
311.
Explanation:
We Follow the same procedure as For the
previous part oF the problem.
±
±
±
~
A
±
±
±
=
q
A
2
x
+
A
2
y
+
A
2
z
=
q
(200)
2

200)
2

300)
2
=412
.
311
.
004 (part 4 of 5) 2.0 points
±ind
±
±
±
~
B
±
±
±
.
Correct answer: 655
.
744.
Explanation:
We Follow the same procedure again.
±
±
±
~
B
±
±
±
=
q
B
2
x
+
B
2
y
+
B
2
z
=
q
(

300)
2
+(500)
2
2
=655
.
744
.
005 (part 5 of 5) 2.0 points
±ind
±
±
±
~
A
±
±
±
+
±
±
±
~
B
±
±
±
.
Correct answer: 1068
.
05.
Explanation:
Here we simply add the values we obtained
in parts 3 and 4:
±
±
±
~
A
±
±
±
+
±
±
±
~
B
±
±
±
.
311 + 655
.
744
=1068
.
05
.
006
10.0 points
Consider the Following fgure:
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View Full Documentpasha (sep635) – HW#11 – Antoniewicz – (56445)
2
~
t
~
r
~
s
Which of the following statements about
the three vectors in the Fgure are correct?
List all that apply, separated by commas.
A
~
s
=
~
t

~
r
B
~
r
=
~
t

~
s
C
~
r
+
~
t
=
~
s
D
~
s
+
~
t
=
~
r
E
~
r
+
~
s
=
~
t
Correct answer: A, B, E.
Explanation:
Vector subtraction can be tricky. Just as
one way to subtract scalar quantities is to add
the negative of the number being subtracted
(
i.e.
,in
s
t
e
ado
f5

3=2w
ec
ou
ldw
r
i
t
e
5+(

3) = 2), we can do the same with
vectors. We start by writing down the Frst
vector. ±or option
A
,theFrstvectorinthe
subtraction is
~
t
,sowedrawit
:
~
t
Then, we add the
negative
of the vector
being subtracted. When we write down

~
r
,it
will be pointing in the opposite direction from
~
r
.W
ep
lace

~
r
’s starting point at the tip of
~
t
,
and from here, we are simply adding vectors:
~
t
~
s

~
r
Notice that the resultant vector,
~
s
,i
sex

actly the same as the original
~
s
in the Fgure
we started with. So
~
t
+(

~
r
)=
~
t

~
r
=
~
s,
and option
A
is true.
±ollowing the same procedure for the re
maining options, we can determine that
A
,
B
,and
E
are true statements, while the oth
ers are false.
007 (part 1 of 3) 4.0 points
Aunitvector
~
v
lies in the
xy
plane, at an angle
of 150
◦
from the +
x
axis, with a positive
y
component. What are the components of the
unit vector ˆ
v
=
h
ˆ
v
x
,
ˆ
v
y
,
ˆ
v
z
i
?
~
v
150
◦
±ind ˆ
v
x
.
Correct answer:

0
.
866025.
Explanation:
~
v
150
◦
sin 150
◦
cos 150
◦
The
x
component of ˆ
v
is given by
ˆ
v
x
=cos150
◦
=

0
.
866025
.
008 (part 2 of 3) 3.0 points
±ind ˆ
v
y
.
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 Fall '08
 Turner
 Pythagorean Theorem, Vectors, Vector Space, Euclidean geometry, Standard basis, pasha

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