scalar quantity
vector quantity
magnitude
resultant vector
graphical addition
zero vector,
Cartesian coordinates
0
r
quadrants
component vector
decomposition
component
unit vector,
or
algebraic addition
j
^
i
^
S U M M A R Y
The goals of Chapter 3 have been to learn how vectors are represented and used.
Important Concepts
A vector
is a quantity described by both a magnitude and a direction.
Unit Vectors
Unit vectors have magnitude 1 and
no units. Unit vectors
and
define the directions of the
x
 and
y
axes.
j
^
i
^
Using Vectors
Components
The component vectors are parallel to the
x
 and
y
axes:
In the figure at the right, for example:
Minus signs need to be included if the vector points
down or left.
u 5
tan
2
1
(
A
y
/
A
x
)
A
y
5
A
sin
u
A
5
"
A
2
x
1
A
2
y
A
x
5
A
cos
u
A
r
5
A
r
x
1
A
r
y
5
A
x
i
^
1
A
y
j
^
Working Graphically
Working Algebraically
Vector calculations are done component by component:
The magnitude of
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 Spring '08
 Dick
 Physics, Linear Algebra, Addition, Vector Space, Elementary arithmetic, Standard basis, component vectors Ax

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