Ch1H1 – florin – (56950)
1
This printout should have 30 questions.
Multiplechoice questions may continue
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choices before answering.
001 (part 1 of 7) 3.0 points
A proton is located at:
h4 × 10
−
10
m, −1 × 10
−
10
m, 9 × 10
−
10
mO .
Find ~r, the location of the proton from
the origin where ~r = hr
x
, r
y
, r
z
O.
What is r
x
in meters?
Your answer must be within ±
5.0% Correct answer: 4 × 10
−
10
m.
Explanation:
The
position
of
the
proton
is
the
vector from the origin to the location of
the proton. In this case:
h4 × 10
−
10
m, −1 × 10
−
10
m, 9 × 10
−
10
mO
002 (part 2 of 7) 3.0 points
What is r
y
in meters?
Your answer must be within ±
5.0% Correct answer: −1 × 10
−
10
m.
Explanation:
The
position
of
the
proton
is
the
vector from the origin to the location of
the proton. In this case:
h4 × 10
−
10
m, −1 × 10
−
10
m, 9 × 10
−
10
mO
003 (part 3 of 7) 3.0 points
What is r
z
in meters?
Your answer must be within ±
5.0% Correct answer: 9 × 10
−
10
m.
Explanation:
The
position
of
the
proton
is
the
vector from the origin to the location of
the proton. In this case:
h4 × 10
−
10
m, −1 × 10
−
10
m, 9 × 10
−
10
mO
004 (part 4 of 7) 2.0 points
What is ~r in meters?
Your answer must be within ± 5.0%
Correct answer: 9.89949 × 10
−
10
m.
Explanation:
The magnitude of ~r is found by:
q
~r =
r
x
2
+ r
y
2
+ r
z
2
where:
r
x
= 4 × 10
−
10
m
r
y
= −1 × 10
−
10
m
r
z
= 9 × 10
−
10
m
therefore:
~r = 9.89949 × 10
−
10
m
005 (part 5 of 7) 3.0 points
What is ˆr
x
, the x component of the unit
vector in the direction of ~r?
Your answer must be within ±
5.0% Correct answer: 0.404061.
Explanation:
The unit vector has the form:
ˆr =

~r
~r
.
This means that the x component of the
unit vector is:
ˆr
x
=
r
x
~r
4
× 10
−
10
m
=
9.89949 × 10
−
10
m
=
0.404061
7
(part 6 of 7) 3.0 points
What is ˆr
y
, the y component of the unit
vector in the direction of ~r?
Your answer must be within ±
5.0% Correct answer: −0.101015.
Explanation:
The unit vector has the form:
ˆr =

~r
~r
.
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View Full DocumentCh1H1 – florin – (56950)
2
This means that the y component of the
unit vector is:
ˆr
y
=
r
y
~r
−1 × 10
−
10
m
=
9.89949 × 10
−
10
m
=
−0.101015
8
(part 7 of 7) 3.0 points
What is ˆr
z
, the z component of the unit
vector in the direction of ~r?
Your answer must be within ±
5.0% Correct answer: 0.909137.
Explanation:
The unit vector has the form:
ˆr =

~r
~r
.
This means that the z component of the
unit vector is:
ˆr
z
=
r
z
~r
9
× 10
−
10
m
=
9.89949 × 10
−
10
m
=
0.909137
9
(part 1 of 5) 10.0 points
A
planet is located at
~
10
10
10
P
= h−3 × 10
, 5 × 10
, −5 × 10
O.
A star is located at
~
10
10
10
S = h4 × 10
, −7 × 10
, 1 × 10
O.
What is
~
, the vector pointing from the planet
R
to the star?
~
10
11
10
1. R = h7 × 10
, −1.2 × 10
, 7 × 10
O
~
10
11
10
2.
R
=
h7 × 10
, −1.2 × 10
, 6 × 10
O
correct
~
10
11
10
3. R = h5 × 10
, −1.2 × 10
, 3 × 10
O
~
10
11
10
4. R = h5 × 10
, −1.3 × 10
, 4 × 10
O
5. ~
= h9 × 10
−7 × 10
5 × 10
O
R
,
,
Explanation:
This
is
a
vector
subtraction
problem.
To
find
~
, we subtract
~
−
~
by respective com
R S P ponents:
S
x
− P
x
= 4 × 10
10
− (−3 × 10
10
) = 7 × 10
10
S
y
− P
y
= −7 × 10
10
− (5 × 10
10
) = −1.2 × 10
11
S
z
− P
z
= 1 × 10
10
− (−5 × 10
10
) = 6 × 10
10
So
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 Spring '08
 Turner
 Vector Space, Cartesian Coordinate System, René Descartes, Correct Answer, Ry

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