Notes for Unit
: Introduction to Vectors
Introduction to Vectors
.
What is a vector?
A
vector
is a way of representing a straight line segment by describing the “motion” of the segment without reference
to its speci c endpoints.
Examp e
Examp e
Examp e :
In the diagram shown on
the le , point
A
is located at
(
,
)
, and point
B
is
located at
(
,
)
. We can describe
→
AB
as a
motion
that travels

units in the
x
direction, and
units in the
y
direction. We write,
→
AB
=

,
.
e arrow over
→
AB
indicates that the motion
started at
A
and ended at
B
. We’ll use angle
brackets to indicate the coordinates of a vector
(although this notation is not universal).
Examp e
:
In this example,
→
AB
=
,
, and
→
CD
=
,
also.
ey are di erent
line segments
,
but they represent the same
motion
, so they have
the same vector coordinates.
.
Determining the coordinates of a vector
If we know the points where a vector begins and ends, we can subtract the tail from the head to
nd the coordinates of
the vector:
vector
=
head

tail
Examp e
:
Point
A
is
located at
(

,
)
and point
B
is located at
(
,
)
. Find the coordinates of
→
AB
.
So ution:
→
AB
=
B

A
=
,
 
,
=
,

.
Vector Addition and Sca ar Mu tip ication
We can add and subtract vectors by adding and subtracting their individual components. We can also multiply a vector
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 Fall '06
 TWKnott
 Linear Algebra, Vector Space

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