Name
Math
252:Quiz
#1
1)
Given
the
vector
v =
(2,5,l)
,
Normalize
the
vector.
^

\7
1
z
v
CT)
z
t
C
Q
7
b)
Find
a
vector
in the
opposite direction
of
magnitude
v/5
.
2)
a)
Find
the
angle between
the two
vectors
u
=_(2,5,7)
and
v=(0,5,4).

I
tf
\lvi
cose
^
'•'
v/to*
•»(.$>*+
<?>
•=
TlMTFTi
=
vT^s,
^
\/3Tis
''"
5"'
(

2
~~
^
b)
Find
the
angle
the
vector
v
makes with respect
to the
Xaxis. Hint: Consider
(1,0,0)
^
8
'4.
5"
2
<
^
IV
"""I
y
=
(2,3)
and v

(5,1) Find,
>
—>
a) The
projection
of
u
onto
v
.(A
scalar)
b)
The
component
of
u
onto
v ( A
vector)
—»
—>
c) The
orthogonal component
of
u
with respect
to v .
V
7
&
JJ1N
>
r.
/
~>
c,
/
/J
'
4)
Find
the
value
of the
constant
k
which
will
make
the
vectors
(2k,
5,0)
and
(
1,3,2
perpendicular.
Hint: Consider
the dot
product.
C0
1
Cs)CO
t
5)
Write
the
equation
of the
sphere with center
of
C(l,4,3)
if the
point P(10,4,0)
is
on the
sphere.
f
Oo^H
,
o^
of
^
Cx0't
+
o
2
1C,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Name
Math
252
Quiz
on
Directional Derivatives
Suppose
you are
climbing
a
hill
whose
shape
is
given
by
z =
2x
2

4y
2
+35
You
are
standing
at the
point given
by
(1,1,29)
a)
How
fast
is the
slope
of the
surface increasing
in the
direction
of
(2
3 > ?
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 CRAUST
 Force, Acceleration Normal Acceleration

Click to edit the document details