MCV4U1 - UNIT SIX LESSON THREE
LESSON 3: SCALAR MULTIPLICATON OF A VECTOR
Collinear Vectors: Vectors that are parallel. Collinear vectors can be
shifted (translated) so that they lie along the
same straight line.
Unit Vector: A unit vector is a vector that has a magnitude of one. (i.e., 1 metre (m),
1 Newton (N), 1 km/h)

A unit vector, â , in the same direction as a can be expressed using the following
formula:

a
aˆ  
a
Compass Directions for vectors:
r
u
W
N
E
30

S
r
We can express the direction of vector u in the following ways:
1. W30N
2. N60W
3. 30 north of west

4. 60 west of north
5. a bearing of 300 (note: bearing is measured clockwise from the north axis)
Scalar multiplication of a vector:
Ex. Given vector
a)

2u

u
below, with length 3 cm, draw the following vectors:
b)
2
u
3
c)

 5u
d)
1 
u
2
MCV4U1 - UNIT SIX LESSON THREE

u

 5u
2
u
3

2u




Ex. Given vectors a and b , draw a diagram to represent 3a  2b .

a

b

Ex. The vectors u and v are unit vectors that make an
 
angle of 60˚ with each other. Calculate 3u  2v

u
60

v
1 
u
2