Calc10_2 - 10.2 Vectors in a Plane Mesa Verde National Park...

10.2 Vectors in a Plane
Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2003
Mesa Verde National Park, Colorado

Warning:
Only some of this is review
.

Quantities that we measure that have magnitude but
not direction are called scalars .
Quantities such as force, displacement or velocity
that have direction as well as magnitude are
represented by directed line segments .
A
B
initial
point
terminal
point
AB
uuu v
The length is
AB
uuu v
→

A
B
initial
point
terminal
point
AB
uuu v
A vector is represented by a directed line segment.
Vectors are equal if they have the same length and
direction (same slope).
→

A vector is in standard position if the
initial point is at the origin.
x
y
( 29
1 2
, v v
The component form of this vector is:
1 2
, v v = v

A vector is in standard position if the
initial point is at the origin.
x
y
( 29
1 2
, v v
The component form of this vector is:
1 2
, v v = v
The magnitude (length) of
1 2
, v v = v
is:
2 2
1 2
v v = + v
→

P
Q
(-3,4)
(-5,2)
The component form of
PQ
uuu v
is:
2, 2 = - - v
v
(-2,-2)
( 29 ( 29
2 2
2 2 = - + - v
8 =
2 2 =
→

If
1 = v
Then
v
is a unit vector .