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Math 22
Exam 1C
Akers — FS 00
1)
(15 pts)
Given
$
$
23
ai jk
=+
$
and
1,0,4
b
=
1,1,1
c
=
,
find the following:
a) A vector perpendicular to both
a
b
.
b) The scalar projection of
b
in the direction of
a
.
c) A unit vector in the direction of
b
.
d) The angle between
a
b
.
e) Prove
a
is orthogonal to
c
.
2.(8 pts)
Given the vectors
p
q
below,
geometrically show
pq
+
,
2

, and
×
.
3.(10 pts)
Find the equation of the plane that contains both the point (1, 2, 1)
and
the
line
defined parametrically by
1
xt
,
yt
=
,
and
3
zt
.
4. (9 pts)
Match the names of the following surfaces and the axis of orientation
(axis of
symmetry),
and then choose one of the surfaces and sketch it.
Label the graph with the chosen equation.
Surface
Name
Axis
22
30
x yz
+=
_______
____
a.
ellipsoid
b.
cone
c.
parabolic cylinder
2
3
+=
_______
____
d.
hyperbolic paraboloid
e.
elliptic paraboloid
f.
hyperboloid of 1 sheet
222
3
10
xyz
+ +=
_______
____
g.
hyperboloid of 2 sheets
5a. (7 pts)
Find the distance from the point
(1,1,2)
to the plane
28
x
yz
.
5b. (8 pts)
Find
the point (x,y,z)
on the plane in problem #5 that is closest to the
point
(1,1,2).
HINT:
Consider the line L that contains the point
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.
 Winter '08
 BRIGHAM
 Math, Scalar

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