DiscGQ05
–
gilbert
–
(55035)
1
This
printout
should
have
4
questions.
Explanation:
Multiplechoice
questions
may
continue
on
After completion of squares
the
next
column
or
page
–
find
all
choices
x
2
+ y
2
+ z
2
−
6x + 2y
−
8z + 17
=
0
before answering.
001
10.0 points
Which one of the points
P (
−
1, 1,
−
3), Q(3, 6, 6), R(
−
2, 8, 4) in
3space is closest to the xyplane?
1. P (
−
1, 1,
−
3) correct
2. R(
−
2, 8, 4)
3. Q(3, 6, 6)
Explanation:
The distance of a point (a, b, c) in 3
space from the xyplane is given by c.
Consequently, of the three points
P (
−
1, 1,
−
3), Q(3, 6, 6), R(
−
2, 8, 4)
the one closest to the xyplane is
P (
−
1, 1,
−
3)
.
keywords:
plane, distance in 3space,
002
10.0 points
Find the center of the sphere given by
x
2
+ y
2
+ z
2
−
6x + 2y
−
8z + 17 = 0 .
1. center
=
(6,
−
2, 4)
2. center
=
(3,
−
1, 4) correct
3. center
=
(
−
3, 1,
−
4)
4. center
=
(6,
−
2, 8)
5. center
=
(
−
3,
−
1,
−
4)
6. center
=
(3, 1, 8)
becomes
(x
−
3)
2
+(y+1)
2
+(z
−
4)
2
+17
−
9
−
1
−
16 = 0 ,
which can then be written as
(x
−
3)
2
+ (y + 1)
2
+ (z
−
4)
2
=
9 .
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 Spring '07
 Sadler
 3space

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