MCV4U1 – UNIT SIX LESSON ONE
Lesson One: Introduction to Vectors
A vector is a mathematical object that has magnitude (size) and direction.
A scalar has magnitude only.
Vector
Velocity
“The car was travelling 60 km/h north.”
Displacement
“I walked 3 km south-east to school.”
Force
Scalar
Speed
“The car was travelling 60 km/h.”
Distance
“I walked 3 km to school.”
Temperature
Acceleration
Time
We can use one letter or two letters to represent our vector, as long as we put an arrow head on top.
Tail (initial point)
A
Head (terminal point)

u
B
We can call this vector by using its initial and terminal points AB (in that order), or by using an arbitrary

lower case letter, such as u .
The length of the arrow represents the vector’s magnitude. Magnitude is indicated by placing absolute value



bars around the vector. So, u means the magnitude, or length, of the vector u .
The direction of the arrow represents the vector’s direction.
Equality of Vectors:


Two vectors a and b are equal IFF....
 
1. Their magnitudes are equal. a  b
Opposite Vectors:
Two vectors are opposite if they have the same
magnitude, but point in opposite directions.
(They are anti-parallel.)


2. a and b have the same direction.
Opposite
Equal
MCV4U1 – UNIT SIX LESSON ONE


b) Draw any vector PQ and then its opposite QP .

Ex. 1 a) Draw any vector XY .
Ex.
a) State two pairs of equivalent vectors.
b) State two pairs of opposite vectors.
F
R
O
U
Ex. Calculate the following magnitudes, using the diagram below.
a) TV
b) QV
W
c) PV
V
4
3
T
U
15
R
P
S
Q