moseley (cmm3869) – HW10 – Gilbert – (56380)
1
This printout should have 10 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
Which oF the Following statements are true For
all lines and planes in 3space?
I.
two planes perpendicular to a third plane
are parallel
,
II.
two lines parallel to a third line are
parallel
,
III.
two lines perpendicular to a plane are
parallel
.
1.
all oF them
2.
I only
3.
II only
4.
I and II only
5.
III only
6.
II and III only
correct
7.
none oF them
8.
I and III only
Explanation:
I. ±ALSE: the
xy
plane and
yz
plane are
both perpendicular to the
xz
pane, but are
perpendicular to eachh other, not parallel .
II. TRUE: each oF the two lines has a direc
tion vector parallel to the direction vector oF
the third line, so must be scalar multiples oF
each other.
III. TRUE: the two lines will have direction
vectors parallel to the normal vector oF the
plane, and so be parallel, hence the two lines
are parallel.
002
10.0 points
Which oF the Following surFaces is the graph
oF
6
x
+ 4
y
+ 3
z
= 12
in the frst octant?
1.
x
y
z
2.
x
y
z
correct
3.
x
y
z
4.
x
y
z
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2
5.
x
y
z
6.
x
y
z
Explanation:
Since the equation is linear, it’s graph will
be a plane. To determine which plane, we
have only to compute the intercepts of
6
x
+ 4
y
+ 3
z
= 12
.
Now the
x
intercept occurs at
y
=
z
= 0,
i.e.
at
x
= 2; similarly, the
y
intercept is at
y
= 3, while the
z
intercept is at
z
= 4. By
inspection, therefore, the graph is
x
y
z
003
10.0 points
Find parametric equations for the line pass
ing through the point
P
(1
,
−
2
,
3) and parallel
to the vector
a
2
,
1
,
−
3
A
.
1.
x
= 2 +
t, y
= 1
−
2
t, z
=
−
3 + 3
t
2.
x
= 1 + 2
t, y
=
−
2 +
t, z
= 3
−
3
t
correct
3.
x
= 1
−
2
t, y
= 2
−
t, z
= 3
−
3
t
4.
x
= 2 +
t, y
= 1 + 2
t, z
= 3
−
3
t
5.
x
= 2
−
t, y
=
−
1 + 2
t, z
=
−
3 + 3
t
6.
x
=
−
1 + 2
t, y
= 2 +
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 Spring '07
 Sadler
 Multivariable Calculus, direction vector, Moseley

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