GCSE MATHS • HIGHER TIER
Vector Arithmetic Made Simple
Add, subtract and scale vectors accurately, then use them to describe movement and vector journeys.
Clear method
Exam practice
Worked proofs
Vector Arithmetic in Four Moves
1
Read
Identify the horizontal and vertical components of each vector.
2
Operate
Choose whether to add, subtract or multiply by a scalar.
3
Calculate
Work component by component, taking care with negative numbers.
4
Check
Confirm both components and the direction of the resulting vector.
What You’ll Learn
Understand what a vector is.
Read vectors written in column form.
Add vectors component by component.
Subtract vectors accurately.
Key Rules
A vector has both magnitude and direction.
Vectors are usually written using horizontal and vertical components.
When subtracting vectors, subtract the matching components.
When subtracting vectors, subtract the matching components.
Always work component by component.
Worked Proof: Vector Arithmetic
Step-by-Step Method
- 1. Read both components carefully.
- 2. Identify the required operation.
- 3. Work with the horizontal components.
- 4. Work with the vertical components.
- 5. Check signs, especially negative values.
- 6. Write the final vector clearly.
More Worked Examples
1
Add the vectors (3, 2) and (1, 4).
Top: 3 + 1 = 4
Bottom: 2 + 4 = 6
2
Add the vectors (5, −1) and (2, 3).
Top: 5 + 2 = 7
Bottom: −1 + 3 = 2
3
Subtract (2, 1) from (6, 5).
Top: 6 − 2 = 4
Bottom: 5 − 1 = 4
4
Subtract (4, 5) from (7, 3).
Top: 7 − 4 = 3
Bottom: 3 − 5 = −2
- Common GCSE Mistakes
- Adding or subtracting the wrong components.
- Making sign errors with negative numbers.
- Multiplying only one component by a scalar.
- Confusing vector direction when describing a journey.
- Writing the final components in the wrong order.
- Exam Tips
- Keep horizontal and vertical components aligned.
- Work one component at a time.
- Use brackets around negative numbers when multiplying.
- When subtracting, check every sign carefully.
- Multiply every component when using a scalar.
- For vector journeys, follow the route in the correcFor vector journeys, follow the route in the correct order.t order.
Skills Used in Vector Arithmetic
Vectors
Vector Components
Addition
Subtraction
Scalar Multiplication
Negative Numbers
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Vector Arithmetic Tutorial
Step-by-step walkthroughs of Vector Arithmetic with clear methods and exam tips.
Frequently Asked Questions
A vector is a quantity with both magnitude and direction.
Add corresponding horizontal components and corresponding vertical components.
Subtract corresponding components, taking particular care with negative numbers.
A scalar is an ordinary number used to multiply every component of a vector.
Add consecutive journey vectors to find the overall movement from the starting point to the finishing point.
It is the foundation for more advanced GCSE vector geometry and geometric vector proofs.