Vectors have both magnitude and direction, while scalars only have magnitude; displacement is a vector that describes the change in position between an initial and final location. The document covers vector addition and subtraction using diagrams, as well as multiplying, dividing, and finding the x- and y-components of vectors.

1. Chapter 8 Vectors
Physics 504

2. Scalars and Vectors
 A scalar quantity has a size
and unit.
 E.g. 16 N (Newtons)
 A vector quantity has a size,
unit and direction.
 E.g. 5 km/h [N] (North)

3. Distance and Displacement
 Distance travelled depends on
position.
 Distance is a scalar quantity.
 It is always positive.
 E.g. d = 5 km

4. Distance and Displacement
 Displacement depends on the
new position compared to the
old position.
 Displacement is a vector
quantity.
 E.g. Δd or đ = 5 km North

5. Exam Question
The following graph represents the trail followed by a hiker going from A to F (A –> B –> C –> D –
> E –> F). One centimetre represents 100 metres.
What is the displacement of the hiker?
A) 1 700 m
B) 700 m
C) 500 m
D) 200 m

6. The Cardinal Points


7. Cardinal Points II
 Never Eat Slimey Worms
 ½ way between North [N]
andWest [W] is NorthWest
[NW]
 ½ way between NW and N is
NNW

8. Trigonometric Direction
 [East] = 0°
 [North] = 90°
 [West] = 180°
 [South] = 270°

9. Cardinal and Degrees
 [N 45 ° E] means you start at
North and turn 45 ° East.
 It is also known as NE.
 Or as 45 °

10. Vector Addition
 We can show vectors as
arrows in diagrams.
 We add vectors tip to tail.
 Vector Ả +Vector B = Vector B + Vector Ả
 The result of adding two or more vectors is the
RESULTANT VECTOR.
 Vectors are written with little arrows on top.

11. Vector Diagrams

12. Vector Subtraction
 To subtract a vector from
another, you add the
opposite.
 Vector A – Vector B
 = Vector A + (-Vector B)

13. Activity
 Page 189, Q 1 – 6
 Page 192, Q 1 – 3
 Page 195, Q 1 – 4
 Page 197, Q. 1 - 2

14. Multiplying Vectors
 Multiplying vectors only
changes magnitude not
direction (if positive).
 ā = (1,2); 3 ā = (3,6)
 đ = 5 km 45°;
 2đ = 10 km 45°

15. Vector Division
 It is just like vector
multiplication, but with a
fraction.
 N.B. multiplying by a negative
 ř = (3,2); - ř = (-3,-2)
 Ŝ = 2 m [N]; -ŝ = 2m [S]

16. x-Component of a Vector
 ā-hyp opp
 Θ y-part
 adj x – parts
 Cos θ = adj/hyp = x/ā
 Thus, x = ā cos θ

17. y-Component of a Vector
 ā-hyp opp
 Θ y-part
 adj x – parts
 sin θ = opp/hyp = x/ā
 Thus, y = ā sin θ

18. Addition of Vectors:
Component Method
 Add the x-components of the
vectors together.
 Add the y-components of the
vectors together.
 Add the total x vector to the
total y vector tip to tail.

19. Tools for Solving
 You can use diagrams;
 Pythagoras c2 = a2 + b2;
 Sine Law
 Cosine Law
 SOHCAHTOA

20. Summary
 Some motions can be seen
easily; other motions must be
observed using other senses
or devices.
 The trajectory is the path of a
moving object.

21. Summary
 Vector quantities have
magnitude and direction.
 Scalar quantities only have
magnitude.
 Displacement, or change in
position, is a vector quantity.

22. Summary
 Distance, the path length, is a
scalar quantity.
 Add vectors tip to tail.
 Page 199, Q 1 - 5

23. Activity
 Design an Amazing Race