3.1 – Scalars & Vectors

Scalars

Definition: Scalar Quantities
A scalar quantity is a physical quantity that has only magnitude.

Examples of scalars: distance, mass, time, temperature.

Adding scalars follows simple algebraic addition.

Example: Adding Scalars
A person has 2 kg of sugar. You give them 3 kg of sugar. How much sugar do they have now?

2 kg + 3 kg = 5 kg

i.e the answer is found from simple arithmetic addition.

Vectors

Definition: Vector Quantities
A vector quantity is a physical quantity that has both magnitude and direction.

Examples of vectors: displacement, velocity, acceleration, force (e.g weight, friction, air resistance, etc).

Representing Vectors 

A vector can be represented by an arrow drawn with a specific direction, as shown in the following diagram.

 

Adding vectors follows vector addition and must take direction into account.

Example: Adding Vectors
A person walks 3 km away from their home. They then walk another 2 km. How far could they be from their home?

If they had continued to walk in the same direction:

3 km + 2 km = 5 km

They will be  5 km away from their home.

If they turned around and walked back towards their home:

3 km − 2 km = 1 km

They will be  1 km away from their home.

So, depending on the directions, 3 km added to 2 km could be anywhere from 1 km to 5 km.

We will look at this in more detail in the next chapter.

 

Vector Addition: Triangle (Polygon) Method

  1. Draw the first vector v1 from point A.
  2. Then continue to draw the second vector v2 in a direction away from A, ending at B (Figure 1).
  3. Draw the resultant vector R, from A towards B, and add arrows.
  4. R is the resultant of adding vectors v1 and v2.

The order in which the vectors are added does not matter as can be seen in the diagram below – which gives the same resultant vector, R.

For a more detailed look at vector addition see:
6.7 – vector addition
Kinematics Next >>

 

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