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1
Chapter 3
Vectors
Geometric vector addition and subtraction
¾
Resolving a vector into its components
¾
The notion of a unit vector
¾
Add and subtract vectors by components
¾
Multiplication of a vector by a scalar
¾
The scalar (dot) product of two vectors
¾
The vector (cross) product of two vectors
2
A
scalar
quantity is one that can be described
by a single number:
temperature, speed, mass
A
vector
quantity deals inherently with both
magnitude and direction:
velocity, force, displacement
3
Often it is necessary to add one vector to another.
4
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2.00 m
6.00 m
()
22
2
2.00 m
6.00 m
2.00 m
6.00
6.32m
m
R
R
R
=+
=
θ
1
tan
2.00 6.00
tan
2.00 6.00
18.4
−
=
==
D
6
Geometric vector Subtraction
We write:
From vector
Then we add
to vector
we find
=−=+−
−
−
=−
daba b
d
bb
a
ba
b
GG
G
G
G
G
G
G
Note:
We can add and subtract vectors using the method of
components.
7
A
B
C
A component of a vector along an axis
is the projection
of the vector on this axis.
For example
is the
projection of
along the xaxis.
The component
is defined by drawing straight lines fr
x
x
a
a
a
G
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 Spring '10
 Cohen
 Physics

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