AN INTRODUCTION TO VECTORS
(Geometric Vectors)
A.
VECTORS as DIRECTED LINE SEGMENTS
A scalar quantity possesses magnitude only. (Ex. speed, time)
A vector quantity possesses both magnitude and direction. (Ex. velocity, force)
Ex. 
State whether the following is a vector or a scalar:
a)
a car travelling at 50 km/h to the east
_________________________
b)
a man with a mass of 88 kg
_________________________
c)
a woman skiing at 25 km/h
_________________________
d)
a wagon being pulled with a force of
100N at an angle of 30o to the ground
_________________________
Vectors are represented by a directed line segment.
HEAD (terminal point)
TAIL (initial point)
The length of the line segment is proportional to the magnitude of the vector.
The direction of the line segment is the direction of the vector.
NOTATION

a
“point to point vector”
B
AB
or
A
initial
point
Are AB and BA the same vector?
terminal
point
MAGNITUDE and DIRECTION
y
Magnitude
P(a,b)
Direction
𝑢 = 𝑂𝑃
u
tan𝜃 =
=
0≤𝜃≤𝜋
x
O
u  OP
Since OP has its tail at the origin, OP is called a position vector.
B.
EQUALITY of VECTORS
Two vectors are equal (or equivalent) if and only if
(iff) they have the same magnitude and direction.
B
u
D
v
u  v or AB  CD
AB  CD
A
C
Equal vectors can be translated to be coincident with each other.
OPPOSITE VECTORS
Two vectors that are opposite have the same magnitude but point in opposite
directions.
B
B
u  v or AB  BA
u
v
A
A
Ex 
A
ABCDEF is a regular hexagon. Give examples of vectors which are:
C.
equal
b)
parallel but having different magnitudes
c)
equal in magnitude but opposite in direction
d)
equal in magnitude but not parallel
e)
different in both magnitude and direction
B
F
C
E
a)
D
BEARINGS (HEADINGS)
NW
N
NE
W
E
SW
SE
S
Ex 
A cyclist travels due north for 3km and then turns to a heading of SE
and travels for 5km. Draw the corresponding vector diagram.
Homework: p.279–281 #1, 2, 4, 5, 7–10