Edexcel International GCSE Mathematics A · 4MA1
Vectors
A vector describes a displacement with direction and magnitude. Column vectors record horizontal and vertical components separately. Routes with the same start and end points have the same resultant displacement even when their individual steps differ.
Key method
Add corresponding components. To find AB from position vectors a and b, calculate b − a. Reversing a vector changes the sign of both components.
Worked example
A has position vector (2, −1) and B has position vector (7, 3). Find AB.
- Subtract A’s horizontal coordinate from B’s: 7 − 2 = 5.
- Subtract A’s vertical coordinate from B’s: 3 − (−1) = 4.
- Interpret the result as five units right and four units up.
Answer and interpretation
AB = (5, 4), with magnitude √41.
Common mistake
Calculating a − b gives BA, the displacement in the opposite direction.
Practise independently
If u = (3, −2) and v = (−1, 4), find 2u + v.
Check your answer
(6, −4) + (−1, 4) = (5, 0).
Syllabus connection
This lesson develops vector arithmetic within the geometry area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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