MATH 210
Sample exam problems for the 1st hour exam
Fall 2009
1. Let
A
= (1
,
−
1
,
2)
, B
= (0
,
−
1
,
1)
, C
= (2
,
1
,
1).
(a) Find the vector equation of the plane through
A,B,C
.
(b) Find the area of the triangle with these three vertices.
2. Find the vector of length one in the direction of
−→
v
−
−→
u
where
−→
v
=
a
7
,
5
,
3
A
and
−→
u
=
a
4
,
5
,
7
A
.
3. Let
−→
r
(
t
) =
a
3
t
−
1
,e
t
,
cos(
t
)
A
.
(a) Find the unit tangent vector
−→
T
to the path
−→
r
(
t
) at
t
= 0.
(b) Find the speed,
v
v
v
v
−→
r
′
(
t
)
v
v
v
v
at
t
= 0.
4. Given a point
P
= (0
,
1
,
2) and the vectors
−→
u
=
a
1
,
0
,
1
A
and
−→
v
=
a
2
,
3
,
0
A
, ±nd
(a) an equation for the plane that contains
P
and whose normal vector is perpendicular to
the two vectors
−→
u
and
−→
v
,
(b) a set of parametric equations of the line through
P
and in the direction of
−→
v
.
5. Find the speed and arclength of the path
−→
r
(
t
) =
a
3 cos
t,
4 cos
t,
5 sin
t
A
where 0
≤
t
≤
2.
6. Find the curvature at
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This note was uploaded on 07/06/2011 for the course MATH 210 taught by Professor Slodowski during the Fall '08 term at Ill. Chicago.
 Fall '08
 SLODOWSKI
 Math, Calculus

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