AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Calculations will be limited to two vectors at right angles.
Full specification wording
Scalars and vectors: Calculations will be limited to two vectors at right angles.
This statement defines the scope of vector calculations for perpendicular vectors.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 10
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
This statement defines the scope of vector calculations for perpendicular vectors. When combining two vectors at 90° to each other, you draw a right-angled triangle with the vectors placed tip-to-tail. You then use Pythagoras' theorem to find the magnitude of the resultant and an inverse tangent to find its direction. For example, a 3.0 N force north and a 4.0 N force east give a resultant of 5.0 N at 37° from the 4.0 N force. Resolving a single vector into two perpendicular components is the reverse process, using sine and cosine. While equilibrium problems can involve three coplanar forces, calculations to resolve them will rely on breaking them down into two perpendicular axes or using a closed vector triangle.
What earns the marks
- State that the two vectors must be perpendicular to form a right-angled triangle.
- Use Pythagoras' theorem to calculate the magnitude of the resultant from two perpendicular vectors.
- Use an inverse tangent ratio to calculate the angle giving the direction of the resultant relative to one of the vectors.
- Resolve a single vector into two perpendicular components using sine and cosine.
- For three coplanar forces in equilibrium, resolve them into two perpendicular axes to simplify calculations.
Common mistakes and how to put them right
Adding the two magnitudes arithmetically instead of combining them as perpendicular vectors.
Put it right by using Pythagoras' theorem so the resultant is larger than either vector but smaller than their sum.
Using the wrong trigonometric ratio when finding the angle.
Put it right by identifying which sides are opposite and adjacent to the required angle before choosing tangent.
Forgetting to state the direction of the resultant.
Put it right by giving the angle relative to a named vector or a compass direction.
Exam tips
- Sketch the two vectors tip-to-tail and mark the right angle before substituting numbers.
- Check that the resultant magnitude lies between the larger vector and the arithmetic sum of the two vectors.
Try the lesson
The start of the Scalars and vectors: Calculations will be limited to two vectors at right angles. lesson, made from checked teaching notes for this specification point.
Have a go first
A student walks 3 m due east and then 4 m due north. What is the magnitude of the resultant displacement?
Listen
This statement defines the scope of vector calculations for perpendicular vectors. When combining two vectors at 90° to each other, you draw a right-angled triangle with the vectors placed tip-to-tail. You then use Pythagoras' theorem to find the magnitude of the resultant and an inverse tangent to find its direction. For example, a 3.0 N force north and a 4.0 N force east give a resultant of 5.0 N at 37° from the 4.0 N force. Resolving a single vector into two perpendicular components is the reverse process, using sine and cosine. While equilibrium problems can involve three coplanar forces, calculations to resolve them will rely on breaking them down into two perpendicular axes or using a closed vector triangle. A strong answer earns marks for these points. State that the two vectors must be perpendicular to form a right-angled triangle. Use Pythagoras' theorem to calculate the magnitude of the resultant from two perpendicular vectors. Use an inverse tangent ratio to calculate the angle giving the direction of the resultant relative to one of the vectors. Resolve a single vector into two perpendicular components using sine and cosine. A common slip: Adding the two magnitudes arithmetically instead of combining them as perpendicular vectors. Instead, using Pythagoras' theorem so the resultant is larger than either vector but smaller than their sum. Exam tip: Sketch the two vectors tip-to-tail and mark the right angle before substituting numbers.
See it
Key words
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Vector addition
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Resultant magnitude and direction
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Resolution of vectors
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See every definition
- Vector addition
- Combining two vectors at 90° by drawing a right-angled triangle with the vectors placed tip-to-tail.
- Resultant magnitude and direction
- The size found using Pythagoras' theorem and the angle found using an inverse tangent.
- Resolution of vectors
- The reverse process of resolving a single vector into two perpendicular components using sine and cosine.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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