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Math 192, Prelim 1
September 27, 2007. 7:309:00
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1) The position vector of a moving particle is given by
r
(
t
) = (1 +
t
)
i
+ (
t
2

1)
j
+ 2
t
k
.
a) (6 points) Find the velocity and acceleration vectors.
b) (6 points) Find, as a function of
t
, the cosine of the angle between the velocity and
acceleration vectors.
2) Consider the planes
P
1
and
P
2
given respectively by
x
+ 2
y
+ 3
z

1 = 0 and
x

2
y
= 0.
a) (8 points) Find the point of intersection of
P
2
with the line passing through
A
(1
,
1
,
1) and
B
(2
,
0
,
0).
b) (8 points) Find a parametric equation of the line in which the planes
P
1
and
P
2
intersect.
3) Consider the three points
A, B
and
C
with coordinates (1
,
0
,
2), (

2
,
1
,

1) and (1
,
1
,
1).
a) (8 points) Find the area of the triangle
ABC
.
b) (8 points) Find the distance from
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This note was uploaded on 02/28/2008 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 PANTANO
 Math, Multivariable Calculus

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