moore (jwm2685) – HW08 – gilbert – (55485)
1
This printout should have 23 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
Suppose you start at the origin in 3space,
move along the
x
axis a distance oF 3 units in
the positive direction, and then move down
ward a distance oF 2 units.
What are the coordinates oF your position?
1.
(0
,
3
,
−
2)
2.
(3
,
0
,
−
2)
correct
3.
(3
,
0
,
2)
4.
(3
,
−
2
,
0)
5.
(0
,
−
2
,
3)
Explanation:
We start at the origin, which has coordi
nates (0
,
0
,
0). ±irst we move 3 units along
the positive
x
axis, a²ecting only the
x

coordinate, bringing us to the point (3
,
0
,
0).
We then move 2 units downward, in the nega
tive
z
direction. Thus only the
z
coordinate is
a²ected, and so we arrive at the point having
coordinates
(3
,
0
,
−
2)
.
keywords: 3space, coordinates,
002
10.0 points
Which one oF the points
P
(
−
1
,
9
,
8)
, Q
(3
,
1
,
0)
, R
(5
,
0
,
9)
in 3space is closest to the
yz
plane?
1.
P
(
−
1
,
9
,
8)
correct
2.
Q
(3
,
1
,
0)
3.
R
(5
,
0
,
9)
Explanation:
The distance oF a point (
a, b, c
) in 3space
From the
plane is given by

a

.
Conse
quently, oF the three points
P
(
−
1
,
9
,
8)
, Q
(3
,
1
,
0)
, R
(5
,
0
,
9)
the one closest to the
plane is
P
(
−
1
,
9
,
8)
.
keywords: plane, distance in 3space,
003
10.0 points
A rectangular box is constructed in 3space
with one corner at the origin and other ver
tices at
(4
,
0
,
0)
,
(0
,
3
,
0)
,
(0
,
0
,
5)
.
±ind the length oF the diagonal oF the box.
1.
length =
√
43
2.
length =
√
34
3.
length = 34
4.
length = 5
√
2
correct
5.
length = 50
6.
length = 43
Explanation:
We have to fnd the length oF
BD
in the
fgure
O
D
A
B
G
F
C
E