patino (mp25752) – Assignment3 – luecke – (57510)
1
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printout
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have
11
questions.
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001
10.0 points
Which one of the points
P
(1
,
6
,
4)
,
Q
(9
,
−
8
,
7)
,
R
(
−
5
,
5
,
−
8)
in 3space is closest to the
yz
plane?
1.
P
(1
,
6
,
4)
correct
2.
Q
(9
,
−
8
,
7)
3.
R
(
−
5
,
5
,
−
8)
Explanation:
The distance of a point (
a, b, c
) in 3space
from the
yz
plane is given by

a

.
Conse
quently, of the three points
P
(1
,
6
,
4)
,
Q
(9
,
−
8
,
7)
,
R
(
−
5
,
5
,
−
8)
the one closest to the
yz
plane is
P
(1
,
6
,
4)
.
keywords: plane, distance in 3space,
002
10.0 points
Which of the following statements are true:
A.
in
3
space the pair of equations
braceleftbigg
x
= 5
,
z
= 4
,
represents a line
,
B.
in
2
space the equation
x
= 5
represents a
line
.
1.
both of them
correct
2.
B only
3.
neither of them
4.
A only
Explanation:
A. TRUE:
in
3
space the equation
x
= 5
represents a planeperpendicular tothe
x
axis,
while
z
= 4
represents a plane perpendicular
to the
z
axis.
But together the equations
represent the intersection of these two planes,
i.e.
, a line
.
B. TRUE:
in the plane the graph of
x
= 5
is a vertical line
.
keywords:
T/F, True/False, plane, 2space,
3space, point
003
10.0 points
A triangle Δ
PQR
has vertices
P
(2
,
1
,
−
1)
, Q
(1
,
0
,
2)
, R
(3
,
2
,
2)
.
Use the distance formula to decide which one
of the following properties the triangle has.
1.
isoceles with

QP

=

QR

2.
not isoceles
3.
isoceles with

RP

=

RQ

4.
isoceles with

PQ

=

PR

correct
Explanation:
Recall that for points
A, B
it is common to
denote the line segment from
A
to
B
by
AB
,
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 Spring '09
 Lueke
 triangle, 3space

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