AQA · GCSE · Physics
Course version: 8463 · Version from Sept 2016
The length of the arrow represents the magnitude, and the direction of the…
Full specification wording
Scalar and vector quantities: The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity.
When an arrow represents a vector to scale, its length stands for the magnitude and the way it points stands for the direction.
Checked against the AQA 8463 specification (opens in a new tab) on .
- Point 4 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When an arrow represents a vector to scale, its length stands for the magnitude and the way it points stands for the direction. Start by choosing and writing down a scale, for example 1 cm represents 10 N. A 35 N force then needs a line 3.5 cm long, measured with a ruler, with the arrowhead placed to show which way the force acts. Reading a diagram reverses the process: measure the arrow, then multiply by the scale, so a 4.2 cm arrow on that scale is 42 N. The scale must stay the same for every arrow on the diagram, otherwise a comparison of lengths says nothing about the comparison of magnitudes.
What earns the marks
- Choosing and stating a scale, such as 1 cm represents 10 N.
- A line drawn and measured to the correct length for the magnitude.
- An arrowhead placed to show the direction of the quantity.
- Converting a measured length back to a magnitude using the stated scale.
Common mistakes and how to put them right
Drawing arrows at any convenient length and writing the value beside them instead.
Changing the scale part-way through a diagram, so arrows can no longer be compared.
Measuring the arrow correctly but forgetting to multiply by the scale.
Giving an answer in centimetres rather than converting to newtons or metres per second.
Giving a magnitude with no direction when the question asks for a vector.
Exam tips
- Write the scale on the diagram itself; a scale kept only in your head cannot be credited.
- Choose a scale that makes the longest arrow fill most of the space available, which reduces measuring error.
- Measure to the nearest millimetre and state the answer to a sensible number of figures.
Try the lesson
The start of the Scalar and vector quantities: The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity. lesson, made from checked teaching notes for this specification point.
Have a go first
On an arrow drawn to represent a vector quantity, what does the length of the arrow represent?
Listen
When an arrow represents a vector to scale, its length stands for the magnitude and the way it points stands for the direction. Start by choosing and writing down a scale, for example 1 cm represents 10 N. A 35 N force then needs a line 3.5 cm long, measured with a ruler, with the arrowhead placed to show which way the force acts. Reading a diagram reverses the process: measure the arrow, then multiply by the scale, so a 4.2 cm arrow on that scale is 42 N. The scale must stay the same for every arrow on the diagram, otherwise a comparison of lengths says nothing about the comparison of magnitudes. A strong answer earns marks for these points. choosing and stating a scale, such as 1 cm represents 10 N. a line drawn and measured to the correct length for the magnitude. an arrowhead placed to show the direction of the quantity. converting a measured length back to a magnitude using the stated scale. Exam tip: Write the scale on the diagram itself; a scale kept only in your head cannot be credited.
Key words
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scale drawing
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length represents magnitude
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arrowhead shows direction
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converting back from a measurement
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See every definition
- scale drawing
- A diagram in which the length of the arrow represents the magnitude and the direction of the arrow the direction of the vector quantity.
- length represents magnitude
- The length of the arrow stands for the magnitude of the vector quantity, measured with a ruler against a stated scale.
- arrowhead shows direction
- The arrowhead is placed to show which way the force acts, giving the direction of the vector quantity.
- converting back from a measurement
- Reading a diagram reverses the process: measure the arrow, then multiply by the scale to give the magnitude.
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