Assignment 3.
Lines and Planes
Read 13.5
You should be able to do the following problems:
Section 13.5/Problems 1  58
Hand in the following problems:
1a.
Find the equation of the line that passes through (0
,
0
,
1) and (1
,
0
,
2).
b.
Find the equation of the plane that passes through (1
,
0
,
0) and is perpendicular to the line in
part (a).
2.
The following equation describes a straight line:
)
r
(
t
)=
±
1
,
1
,
0
²
+
t
±
0
,
2
,
1
²
a.
Find the angle between the given line and the vector
)
u
=
±
1
,

1
,
2
²
.
b.
Find the equation of the plane that passes through the point (0
,
0
,
4) and is perpendicular to
the given line.
3.
The following two lines intersect at the point (1
,
4
,
4)
)
r
=
±
1
,
4
,
4
²
+
t
±
0
,
1
,
0
²
)
r
=
±
1
,
4
,
4
²
+
t
±
3
,
5
,
4
²
a.
Find the angle between the two lines.
b.
Find the equation of the plane that contains every point on both lines.
4.
The following equation describes a straight line:
±
x, y, z
²
=
±
1
,
0
,

2
²
+
t
±
1
,
2
,
2
²
Find the coordinates of the point where this line intersects the
y
axis.
5.
There is a plane that contains the
y
axis as well as every point on the line described in problem
4. Find the equation of this plane.