AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Scale drawings may involve vectors at angles other than 90°.
Full specification wording
Scalars and vectors: Scale drawings may involve vectors at angles other than 90°.
This statement extends vector work beyond right angles: when vectors act at any angle, you can find the resultant by drawing them to scale rather than by right-angled trigonometry alone.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 5 of 10
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
This statement extends vector work beyond right angles: when vectors act at any angle, you can find the resultant by drawing them to scale rather than by right-angled trigonometry alone. Choose a scale such as 1 cm = 2 N, draw each vector tip-to-tail at its correct angle using a protractor, then measure the length and direction of the line from start to finish. For example, a 6.0 N force at 0° and a 5.0 N force at 60° can be drawn to scale and the resultant measured, then converted back using the scale. Calculations may also use perpendicular components, but the scale drawing itself is the method assessed here. Accuracy depends on a sharp pencil, a sensible scale and careful measurement.
What earns the marks
- Choose a scale that makes the drawing large enough to measure accurately and state it clearly.
- Draw each vector tip-to-tail at the correct angle using a protractor, with arrows showing direction.
- Measure the length of the resultant from the tail of the first vector to the tip of the last vector.
- Convert the measured length back to the physical quantity using the stated scale.
- Measure the direction of the resultant with a protractor relative to a named reference direction.
- Use perpendicular components as an alternative check when the angle between vectors is not 90°.
Common mistakes and how to put them right
Drawing vectors tail-to-tail instead of tip-to-tail.
Put it right by placing the tail of each new vector at the tip of the previous one.
Using a scale that makes the diagram too small to measure.
Put it right by choosing a scale that gives a drawing of a convenient size.
Measuring the angle from an unstated direction.
Put it right by naming the reference direction, such as the horizontal or the first vector.
Exam tips
- State the scale before drawing so the examiner can follow the conversion from length to magnitude.
- Use a sharp pencil and a protractor, and measure the resultant line as precisely as the scale allows.
- Label the resultant with its arrow and give its direction relative to a clearly named direction.
Try the lesson
The start of the Scalars and vectors: Scale drawings may involve vectors at angles other than 90°. lesson, made from checked teaching notes for this specification point.
Have a go first
Two forces of 50 N and 30 N act on an object, with an angle of 40° between their lines of action. A student determines the resultant by drawing a vector triangle. The 50 N force is drawn as a horizontal line 10.0 cm long. What is the length of the line representing the 30 N force, and what is the interior angle between the two drawn lines?
Listen
This statement extends vector work beyond right angles: when vectors act at any angle, you can find the resultant by drawing them to scale rather than by right-angled trigonometry alone. Choose a scale such as 1 cm = 2 N, draw each vector tip-to-tail at its correct angle using a protractor, then measure the length and direction of the line from start to finish. For example, a 6.0 N force at 0° and a 5.0 N force at 60° can be drawn to scale and the resultant measured, then converted back using the scale. Calculations may also use perpendicular components, but the scale drawing itself is the method assessed here. Accuracy depends on a sharp pencil, a sensible scale and careful measurement. A strong answer earns marks for these points. Choose a scale that makes the drawing large enough to measure accurately and state it clearly. Draw each vector tip-to-tail at the correct angle using a protractor, with arrows showing direction. Measure the length of the resultant from the tail of the first vector to the tip of the last vector. Convert the measured length back to the physical quantity using the stated scale. A common slip: Drawing vectors tail-to-tail instead of tip-to-tail. Instead, placing the tail of each new vector at the tip of the previous one. Exam tip: State the scale before drawing so the examiner can follow the conversion from length to magnitude.
Key words
Say what each word means before you turn the card.
Scale drawing
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Vector addition at any angle
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Measurement accuracy
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See every definition
- Scale drawing
- A method of finding a resultant by drawing vectors to a chosen scale, such as 1 cm = 2 N, and measuring the line from start to finish.
- Vector addition at any angle
- Drawing each vector tip-to-tail at its correct angle using a protractor, with arrows showing direction, when vectors act at angles other than 90°.
- Measurement accuracy
- Dependence on a sharp pencil, a sensible scale and careful measurement, with a scale chosen to make the drawing large enough to measure accurately.
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