Instructor: Dr. Yuli B. Rudyak
MAC 2313, Calculus 3 with Analytic Geometry, Fall 2011
QUIZ 2, SEPTEMBER 21, 2011
Problem 1.
Find parametric equations for the line through
A
(5
,
1
,
0)
that is perpendicular to the plane 2
x

y
+
z
= 1. In what points does
this line intersect the coordinate planes?
Solution:
The direction vector of the target line is the normal vector
of the given plane. So, we know the point (5,1,0) on the line and its
normal vector
h
2
,

1
,
1
i
and get the following parametric equations of
the line
x
= 5 + 2
t
,
y
= 1

t
,
z
=
t
. To ﬁnd intersection point of
the line and the coordinate plane
x
= 0, put
x
= 0 in the equation
x
= 5 + 2
t
and get
t
=

5
/
2. Then
y
= 1

t
= 7
/
2 and
z
=
t

5
/
1.
So, we get the intersection points (0
,
7
/
2
,

5
/
2. The remaining case
can be considered similarly. Answer: for
y
= 0 we have (7,0,1), for
z
= 0 we have (5,1,0).
Problem 2.
Find parametric equations for the line through the point
A
(0
,
1
,
2) that is perpendicular to the line