DiscGQ05 – gilbert – (55035)
1
This
print-out
should
have
4
questions.
Explanation:
Multiple-choice
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
3-space is closest to the xy-plane?
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 xy-plane is given by |c|.
Conse-quently, of the three points
P (−1, 1, −3), Q(3, 6, 6), R(−2, 8, 4)
the one closest to the xy-plane is
P (−1, 1, −3)
.
keywords:
plane, distance in 3-space,
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)