zakaria (mmz255) – HW09 – gilbert – (55485)
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
+ 3
y
+ 4
z
= 12
.
Now the
x
intercept occurs at
y
=
z
= 0,
i.e.
at
x
= 2; similarly, the
y
intercept is at
y
= 4, while the
z
intercept is at
z
= 3. By
inspection, therefore, the graph is
x
y
z
003
10.0points
Find parametric equations for the line pass
ing through the point
P
(4
,
−
4
,
1) and parallel
to the vector
(
1
,
1
,
−
4
)
.
1.
x
= 4 +
t, y
=
−
4 +
t, z
= 1
−
4
t
correct
2.
x
= 4
−
t, y
= 4
−
t, z
= 1
−
4
t
3.
x
= 1 + 4
t, y
= 1 + 4
t, z
= 4
−
t
4.
x
= 1
−
4
t, y
=
−
1 + 4
t, z
=
−
4 +
t
5.
x
=
−
4 +
t, y
= 4 +
t, z
=
−
1
−
4
t
6.
x
= 1 + 4
t, y
= 1
−
4
t, z
=
−
4 +
t
Explanation:
A line passing through a point
P
(
a, b, c
)
and having direction vector
v
is given para
metrically by
r
(
t
) =
a
+
t
v
,
a
=
(
a, b, c
)
.
Now for the given line,
a
=
(
4
,
−
4
,
1
)
,
v
=
(
1
,
1
,
−
4
)
.
Thus
r
(
t
) =
(
4 +
t,
−
4 +
t,
1
−
4
t
)
.
Consequently,
x
= 4 +
t, y
=
−
4 +
t, z
= 1
−
4
t
are parametric equations for the line.
keywords: line, parametric equations, direc
tion vector, point on line
004
10.0points
A line
ℓ
passes through the point
P
(4
,
3
,
2)
and is perpendicular to the plane
x
+
y
−
2
z
= 2
.
At what point
Q
does
ℓ
intersect the
xy

plane?
1.
Q
(5
,
4
,
0)
correct
2.
Q
(4
,
5
,
0)
3.
Q
(3
,
2
,
0)