AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Vector quantities have magnitude and an associated direction.
Full specification wording
Scalar and vector quantities: Vector quantities have magnitude and an associated direction.
A vector is a quantity that is not fully described by its size alone: it also has an associated direction.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 2 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A vector is a quantity that is not fully described by its size alone: it also has an associated direction. Magnitude tells you how much, and direction tells you which way, so both are needed. For example, a force of 20 N acting to the right, a velocity of 15 m/s due north and a displacement of 3 m upwards are vectors. Because direction matters, vectors cannot simply be added as ordinary numbers; two 5 N forces can give a resultant from 0 N to 10 N depending on their directions. Displacement, velocity, acceleration, force, weight and momentum are vectors. In an exam you may need to identify a vector, state its direction, or explain why direction must be given. Always quote magnitude with its unit and then the direction.
What earns the marks
- A vector quantity needs both magnitude and an associated direction to be fully described.
- Magnitude gives the size, such as 20 N or 15 m/s, and direction gives which way it acts or moves.
- Examples of vectors include displacement, velocity, acceleration, force, weight and momentum.
- Vectors cannot be combined by simple arithmetic alone because their directions affect the resultant.
- A direction may be given as left, right, up, down, north, or as an angle from a stated line.
Common mistakes and how to put them right
Giving only a magnitude for a vector, for example 'a force of 20 N' without saying which way it acts.
Put it right: The direction must also be stated.
Treating velocity as a scalar.
Put it right: Velocity is a vector because it includes direction, whereas speed is the scalar.
Adding vector magnitudes as ordinary numbers, for example assuming two 5 N forces always give 10 N.
Put it right: The resultant depends on their directions.
Exam tips
- When identifying a vector, name both parts: give the magnitude with its unit and then the direction.
- Use a clear direction reference such as 'to the right' or '30° above the horizontal' rather than a vague phrase.
- If asked to explain, say that magnitude alone is insufficient because direction is also needed for a complete description.
Try the lesson
The start of the Scalar and vector quantities: Vector quantities have magnitude and an associated direction. lesson, made from checked teaching notes for this specification point.
Have a go first
Force is an example of a vector quantity. Which statement correctly describes what makes force a vector quantity?
Listen
A vector is a quantity that is not fully described by its size alone: it also has an associated direction. Magnitude tells you how much, and direction tells you which way, so both are needed. For example, a force of 20 N acting to the right, a velocity of 15 m/s due north and a displacement of 3 m upwards are vectors. Because direction matters, vectors cannot simply be added as ordinary numbers; two 5 N forces can give a resultant from 0 N to 10 N depending on their directions. Displacement, velocity, acceleration, force, weight and momentum are vectors. In an exam you may need to identify a vector, state its direction, or explain why direction must be given. Always quote magnitude with its unit and then the direction. A strong answer earns marks for these points. A vector quantity needs both magnitude and an associated direction to be fully described. Magnitude gives the size, such as 20 N or 15 m/s, and direction gives which way it acts or moves. Examples of vectors include displacement, velocity, acceleration, force, weight and momentum. Vectors cannot be combined by simple arithmetic alone because their directions affect the resultant. Exam tip: When identifying a vector, name both parts: give the magnitude with its unit and then the direction.
Key words
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Vector quantity
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Magnitude
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Direction
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Resultant
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See every definition
- Vector quantity
- A quantity that has magnitude and an associated direction, so both are needed to describe it fully.
- Magnitude
- The size of a quantity, such as 20 N or 15 m/s, quoted with its unit.
- Direction
- Which way a quantity acts or moves, which may be given as left, right, up, down, north, or as an angle from a stated line.
- Resultant
- What vectors give when combined, which depends on their directions, so two 5 N forces can give from 0 N to 10 N.
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