OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Scalars and vectors: (b) vector addition and subtraction
Vector addition combines two or more vectors to find a resultant, taking direction into account.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Vector addition combines two or more vectors to find a resultant, taking direction into account. For perpendicular vectors, resolve into components and use Pythagoras with trigonometry: a 3 N force east plus a 4 N force north gives a resultant of 5 N at an angle where tan θ = 4 ÷ 3, so θ ≈ 53° from the east direction. For non-perpendicular vectors, draw them tip-to-tail and use the cosine rule or scale drawing. Vector subtraction means adding the negative of the vector: a − b = a + (−b), where −b has the same magnitude as b but the opposite direction. Always state the magnitude and direction of the resultant, and check that the answer is sensible relative to the original vectors.
What earns the marks
- Vector addition must account for direction; magnitudes are not simply added unless the vectors are parallel.
- Perpendicular vectors can be combined using Pythagoras' theorem for magnitude and trigonometry for direction.
- Non-perpendicular vectors can be combined by scale drawing or by resolving into perpendicular components.
- Vector subtraction is addition of the reversed vector: a − b = a + (−b).
- The resultant should be stated with both magnitude and direction, for example 5.0 N at 53° north of east.
- A scale drawing must have a stated scale, and the resultant measured with a ruler and protractor.
Common mistakes and how to put them right
Adding magnitudes directly for perpendicular vectors.
Put it right: 3 N and 4 N at right angles give 5 N, not 7 N.
Forgetting to reverse the second vector in a subtraction.
Put it right: A − b requires the direction of b to be reversed before adding.
Giving only the magnitude of a resultant.
Put it right: A vector answer needs a direction as well.
Using the wrong trigonometric ratio when finding the angle.
Put it right: Check which sides are opposite and adjacent to the required angle.
Exam tips
- Sketch the vectors tip-to-tail before calculating so the geometry is clear.
- For perpendicular vectors, calculate the magnitude with Pythagoras first, then find the direction with tan θ = opposite ÷ adjacent.
- State the direction relative to a named reference direction, such as 40° above the horizontal.
Try the lesson
The start of the Scalars and vectors: (b) vector addition and subtraction lesson, made from checked teaching notes for this specification point.
Listen
Vector addition combines two or more vectors to find a resultant, taking direction into account. For perpendicular vectors, resolve into components and use Pythagoras with trigonometry: a 3 N force east plus a 4 N force north gives a resultant of 5 N at an angle where tan θ = 4 ÷ 3, so θ ≈ 53° from the east direction. For non-perpendicular vectors, draw them tip-to-tail and use the cosine rule or scale drawing. Vector subtraction means adding the negative of the vector: a − b = a + (−b), where −b has the same magnitude as b but the opposite direction. Always state the magnitude and direction of the resultant, and check that the answer is sensible relative to the original vectors. A strong answer earns marks for these points. Vector addition must account for direction; magnitudes are not simply added unless the vectors are parallel. Perpendicular vectors can be combined using Pythagoras' theorem for magnitude and trigonometry for direction. Non-perpendicular vectors can be combined by scale drawing or by resolving into perpendicular components. Vector subtraction is addition of the reversed vector: a − b = a + (−b). Exam tip: Sketch the vectors tip-to-tail before calculating so the geometry is clear.
See it
Key words
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Resultant vectors
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Tip-to-tail addition
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Vector subtraction as reversed addition
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Magnitude and direction of a resultant
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See every definition
- Resultant vectors
- The single vector found by combining two or more vectors, taking direction into account.
- Tip-to-tail addition
- A method for non-perpendicular vectors in which the vectors are drawn tip-to-tail and the cosine rule or a scale drawing is used.
- Vector subtraction as reversed addition
- Adding the negative of the vector, a − b = a + (−b), where −b has the same magnitude as b but the opposite direction.
- Magnitude and direction of a resultant
- Both must always be stated for a resultant, and the answer checked to see that it is sensible relative to the original vectors.
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