1. Definition and Notation
A vector is a quantity that has both size (magnitude) and a direction.
What is a vector?
When do vectors occur?
velocity (direction and speed), force, acceleration, weight
This vector could be written as:
Notation A a a
The magnitude (size) is written as: O

2. Vectors in column form c a 8 from x 4 from y
Write each of the following in column form. d b

3. Multiplying by a scalar
Magnitude of a vector
The magnitude is the vectors size (length) regardless of direction. 3a a a
Find the magnitude of b. Leave your answer as a surd. b

4. Unit vectors b A unit vector has a magnitude of 1 unit.
Check this has one unit:
Consider the vector a from the last slide. 3 4
To find the unit vector of a simply divide the x and y components by the magnitude.
Find the unit vector of b shown below. b

5. Vector addition and subtraction 1
Consider the following two vectors:
Using the column form b a b a 2
How can we represent the red line shown? 8
a+b
How can we represent the red line shown? p
a+b q
How can we represent the red line shown?
-p+q
=p-q

6. Vector addition and subtraction 2
The diagram below shows a parallelogram, OABC, where O is the origin. OA is represented by vector a and OC by vector c.
c) The position vector of B.
Position vector starts at the origin, O.
OB = OA + AB
OB = a + c
d) AC
AC = AO + OC
AC = -a + c
AC = c - a
Given that M is the midpoint of AB find,
e) AM
Using only vectors a and c find the following:
a) AB c
parallel to OC
f) The position vector of M.
b) BC -a
parallel to AO