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AQA A-Level Maths Vectors Questions
Exam-style vectors questions with compact solutions.
AQA A-Level Maths vectors questions usually reward the same habits: define the vector relation clearly, keep the components organised, and show the reason behind each step. Use this page when you want vectors questions for AQA A-Level Maths that feel specific enough to revise from, not like a thin teaser page.
All A-Level Maths boards (AQA, Edexcel, OCR) cover vectors in both pure maths and mechanics. The applications in mechanics, such as resolving forces, are a key part of the applied content.
Updated April 2026
How to use this question set
Do the first two questions without a calculator to check whether your setup and notation are clean. Then move to the ratio and scalar product questions, because those are closer to the questions that usually split comfortable revision from fragile revision.
If you get stuck, read the answer line first, then rebuild the method yourself before looking at the explanation. That keeps the page useful as practice instead of turning it into passive reading.
Practice Questions
1. If a = (2, -1, 4) and b = (5, 3, -2), find a + b and a - b.
Answer: a + b = (7, 2, 2) and a - b = (-3, -4, 6).
Add and subtract matching components only. Keep the brackets visible while you work so the sign changes stay accurate.
2. Find the magnitude of v = (6, -2, 3).
Answer: |v| = 7
sqrt(6^2 + (-2)^2 + 3^2) = sqrt(36 + 4 + 9) = sqrt(49) = 7.
3. Given OA = a and OB = b, express the midpoint of AB as a position vector.
Answer: (a + b) / 2
A midpoint shares the weight equally between the two end points.
4. A point P divides AB internally in the ratio 3:2, so AP:PB = 3:2. Express OP in terms of a and b.
Answer: OP = (2a + 3b) / 5
The point is nearer B, so b gets the larger coefficient only if the ratio is reversed correctly via opposite weights.
5. For p = (1, 2, -1) and q = (4, -1, 2), find p.q.
Answer: p.q = 0
1(4) + 2(-1) + (-1)(2) = 4 - 2 - 2 = 0, so the vectors are perpendicular.
6. If p.q = 12, |p| = 3, and |q| = 5, find the angle between p and q.
Answer: cos(theta) = 12/15 = 4/5, so theta = arccos(4/5) ≈ 36.9 degrees.
This is a scalar product angle question, so start with cos(theta) = (p.q) / (|p||q|).
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Frequently Asked Questions
Are these pages only useful for AQA students?
They are written around the AQA phrasing in the title and examples, but the core vectors methods overlap heavily with Edexcel and OCR. If you take a different board, keep your own specification beside the page and focus on the method and notation.
Should I revise vectors as a separate topic or mixed with mechanics?
Both. Start with vectors as a pure topic so the algebra is clean, then mix it with mechanics and geometry-style questions. That is the safer exam-season pattern because vectors often appear as part of a bigger problem, not as a standalone warm-up.
What matters most for marks in A-Level Maths vectors?
Clear vector setup, correct component arithmetic, and readable reasoning. Students often know the idea but lose marks through sign errors, weak ratio setup, or jumping straight to an answer without showing the vector method.