Name:
MAC 2313
Exam 1 Version A
09/02/2011
SHOW ALL YOUR WORK. Answers without procedure will be graded zero.
[3]1. A vector has initial point
P
(2
,

1
,
3) and terminal point
Q
(1
,
0
,

4). Find its components and a unit
vector with the same direction.
[3] 2. The vector
v
lies on the
xy

plane and makes an angle of
π
4
with the positive
x

axis,

v

= 5, ﬁnd
v
in component form.
[3] 3. Find the equation of the sphere that has points (

2
,
5
,

1) and (6
,
7
,

3) as endpoints of a diameter.
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a) Two lines parallel to a third line are parallel.
b) Given two lines they must either intersect or be parallel.
c) Two lines perpendicular to a third line must be parallel.
[4] 5. Consider the vectors
v
= 3
i

7
j
and
w
=

2
i
+
c
j
, where
c
is some real number.
a) Find a value of
c
such that
v
and
w
are orthogonal.
b) Find a value of
c
such that
v
and
w
are parallel.
[5] 6. Find the area of the triangle with formed by the vectors
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 Spring '08
 Keeran
 Calculus, Geometry, Equations, Vector Motors, Parametric equation, xy −plane

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