1. Scalars
A scalar quantity is a quantity that has magnitude only and has no direction in space
Examples of Scalar Quantities:
Length
Area
Volume
Time
Mass

2. Vectors
A vector quantity is a quantity that has both magnitude and a direction in space
Examples of Vector Quantities:
Displacement
Velocity
Acceleration
Force

3. Vector Diagrams Vector diagrams are shown using an arrow
The length of the arrow represents its magnitude
The direction of the arrow shows its direction

4. Resultant of Two Vectors
The resultant is the sum or the combined effect of two vector quantities
Vectors in the same direction:
6 N 4 N = 10 N
6 m
= 10 m
4 m
Vectors in opposite directions:
6 m s m s-1 = 4 m s-1
6 N 10 N = 4 N

5. The Parallelogram Law The Triangle Law
When two vectors are joined tail to tail
Complete the parallelogram
The resultant is found by drawing the diagonal
The Triangle Law
When two vectors are joined head to tail
Draw the resultant vector by completing the triangle

6. Problem: Resultant of 2 Vectors
2004 HL Section B Q5 (a) Two forces are applied to a body, as shown. What is the magnitude and direction of the resultant force acting on the body?
Solution:
Complete the parallelogram (rectangle)
The diagonal of the parallelogram ac represents the resultant force
The magnitude of the resultant is found using Pythagoras’ Theorem on the triangle abc
12 N a d θ
5 N
13 N 5 b c 12
Resultant displacement is 13 N 67º with the 5 N force

7. Resolving a Vector Into Perpendicular Components
When resolving a vector into components we are doing the opposite to finding the resultant
We usually resolve a vector into components that are perpendicular to each other
Here a vector v is resolved into an x component and a y component v y x

8. Summary
If a vector of magnitude v has two perpendicular components x and y, and v makes and angle θ with the x component then the magnitude of the components are:
x= v Cos θ
y= v Sin θ v
y=v Sin θ y θ
x=v Cosθ