1. Vectors Introduction
Vectors are used to represent quantities that have both a magnitude (size) and direction.
Vectors can be used to represent both 2D and 3D quantities.
There are several ways vectors can be represented.
Diagrammatically
Using ‘column vector’ notation.
Using ‘i-j’ notation.
By specifying a magnitude and direction (e.g. angle).

2. Vector Notation column vector notation i-j notation.
Vectors are printed in bold
(underline handwritten vectors)
j-direction
i-direction

3. Vectors Terminology | Mini Whiteboards
(a) Use i-j notation to write vectors a, b and c.
(b) Use column vector notation to write vectors a, b and c.
(a) a
(b) c b

4. Magnitude and Direction of a Vector
The magnitude of a vector is its length. If
The direction of a vector is the angle it makes with a specified direction.
j-direction
i-direction
In the diagram, a makes an angle of 𝜃° above the direction of i.

5. Magnitude and Direction | Example Problem Pair
Your Turn…
(click)
Find the exact magnitude of the vector
Find the exact magnitude of the vector
and the angle it makes with
and the angle it makes with
the direction of i. +
the direction of i. +
i-direction
i-direction
i-direction

6. Magnitude and Direction | Mini Whiteboards

7. Magnitude and Direction | Example Problem Pair
Your Turn…
(click)
Given a vector
with direction
Vector v has a magnitude 7 and makes an angle of 60° below the i-direction.
30° above the i-direction and magnitude 5, calculate a and b.
Write v as a column vector. + +
i-direction
i-direction
i-direction

8. Vectors | Exercise 15A Main Questions Questions: P293 Answers: P569

9. Vector Operations Vector Addition and Subtraction
Given two vectors
, the following is true:
Simply add or subtract the
i and j components separately.

10. Vector Operations Scalar Multiplication
Given a vector
, the following is true:
Multiply the scalar by each component separately

11. Vector Operations | Mini Whiteboards
Write down these vectors:
(a)
(b)

12. Vector Operations | Mini Whiteboards
Write down these vectors:
(a)
(b)

13. Vector Operations | Mini Whiteboards
, find vector x such that

14. Equal and Parallel Vectors
Two vectors are equal if they have the same magnitude and size.
If a and b are parallel, they can be written as
for some scalar t.
Two vectors do not have to occupy the same position to be equal.

15. Equal and Parallel Vectors| Example
Your Turn…
(click)

16. Equal and Parallel Vectors
A unit vector is a vector with a magnitude of one unit.
To find a unit vector in the direction of a particular vector, divide the vector by its magnitude.

17. Unit Vectors | Example Problem Pair
Your Turn…
(click)
Find the unit vector in the direction of
i-direction

18. Vectors | Activity Matchup Worksheet Questions: P296-297 Answers:
Match each expression from column 1 with one of equal value in column 2.
Exercise 15B
Q5, 7-15

19. Diagrams not accurately drawn
The diagram below is a hexagon ABCDEF.
Write the following vectors in terms of 𝒂 and 𝒃.
Diagrams not accurately drawn 𝒂 A B
𝐴𝐶 =
𝒂+𝒃 𝒃
𝐹𝐷 =
𝒃+𝟑𝒂 𝟒𝒂 C F
𝐹𝐴 =
𝟒𝒂−𝒃−𝒂=
𝟑𝒂−𝒃
𝐷𝐶 =
−𝟑𝒂−𝒃+𝟒𝒂=
𝒂−𝒃 𝒃
𝐴𝐸 =
𝐴𝐹 +𝒃=
− 𝟑𝒂−𝒃 +𝒃 E D 𝟑𝒂
=2𝒃−3𝒂

20. Diagrams not accurately drawn
In triangle ABC, P is a point on 𝐴𝐶 such that 𝐶𝑃 : 𝑃𝐴 = 3:1.
Find 𝐵𝑃 in terms of 𝑚 and 𝑛.
Diagrams not accurately drawn A
𝐶𝐴 =
𝒏+𝒎 P
3 4 𝐶𝐴 =
𝟑 𝟒 𝒏+ 𝟑 𝟒 𝒎
𝐶𝑃 = 𝒎
−𝒏+ 𝟑 𝟒 𝒏+ 𝟑 𝟒 𝒎
𝐵𝑃 = B
= 𝟑 𝟒 𝒎− 𝟏 𝟒 𝒏 𝒏 C

21. Vectors | Activity Card Sort
The A4 sheet contains a diagram showing some vectors. Throughout the task, you may wish to annotate the diagram.
Complete the Tarsia puzzle by referring to the diagram.

22. Displacement and Position Vectors
A vector that represents the displacement between two points is called a displacement vector.
A vector that represents the displacement from a fixed origin is called a position vector.
Understanding the Difference
are position vectors.
are all displacement vectors.

23. Displacement and Position Vectors | Example Problem Pair