Scalars & Vectors
- All quantities can be one of two types:
- A scalar
- A vector
Scalars
- Scalars are quantities that have only a magnitude
- For example, mass is a scalar since it is a quantity that has magnitude without a direction
- Distance is also a scalar since it only contains a magnitude, not a direction
Vectors
- Vectors have both magnitude and direction
- Velocity, for instance, is a vector since it is described with both a magnitude and a direction
- When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling
- For example, the velocity might be 60 km per hour (magnitude) due west (direction)
- Equivalently, the velocity might be –60 km per hour. In this case, the negative sign might indicate the car is travelling to the left, whereas a positive sign would indicate the opposite direction (to the right)
- Distance is a value describing only how long an object is or how far it is between two points - this means it is a scalar quantity
- Displacement on the other hand also describes the direction in which the distance is measured - this means it is a vector quantity
- For example, a displacement might be 100 km north
- Equivalently, a displacement might be +100 km. In this case, the positive sign indicates a direction that might be upwards, whereas a negative sign would indicate downwards
- The table below lists some common examples of scalar and vector quantities:
Scalars & Vectors Table
- Some vectors and scalars are similar to each other
- For example, the scalar quantity distance corresponds to the vector quantity displacement
- Corresponding vectors and their scalar counterparts are aligned in the table where applicable
Worked example
Blu is in charge of training junior astronauts. For one of his sessions, he would like to explain the difference between mass and weight.
Suggest how Blu should explain the difference between mass and weight, using definitions of scalars and vectors in your answer.
Step 1: Recall the definitions of a scalar and vector quantity
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- Scalars are quantities that have only a magnitude
- Vectors are quantities that have both magnitude and direction
Step 2: Identify which quantity has magnitude only
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- Mass is a quantity with magnitude only
- So mass is a scalar quantity
- Blu might explain to his junior astronauts that their mass will not change if they travel to outer space
Step 3: Identify which quantity has magnitude and direction
-
- Weight is a quantity with magnitude and direction (it is a force)
- So weight is a vector quantity
- Blu might explain that to his junior astronauts that their weight - the force on them due to gravity - will vary depending on their distance from the centre of the Earth
Examiner Tip
To help you determine if a quantity is a scalar or vector, just think; can this quantity have a minus sign? For example, can you have negative mass? No. Can you have negative displacement? Yes!
Make sure you are comfortable with the differences between similar scalars and vectors, the most commonly confused pairings tend to be:
- Distance and displacement
- Speed and velocity
- Weight and mass
