plumiVectors in three dimensions: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 10.2 Vectors in three dimensions, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 8 questions on Vectors in three dimensions, as a list
- June 2025, Pure 1, Q10 (6 marks): Given that • PQ → = 2i + 8j – 2k • QR → = 6i + 6k (a) find PR →. (2) (b) Hence show that triangle PQR is both right-angled and isosceles. (4)
- June 2024, Pure 2, Q7 (5 marks): A B l Figure 2 Figure 2 shows a sketch of the straight line l. Line l passes through the points A and B. Relative to a fixed origin O • the point A has position
- June 2023, Pure 1, Q3 (3 marks): Relative to a fixed origin O • the point A has position vector 5i + 3j + 2k • the point B has position vector 2i + 4j + ak where a is a positive integer. (a) Sh
- June 2022, Pure 1, Q9 (6 marks): P S R Q Figure 3 Figure 3 shows a sketch of a parallelogram PQRS. Given that • PQ → = 2i + 3j − 4k • QR → = 5i − 2k (a) show that parallelogram PQRS is a rhombu
- June 2022, Pure 2, Q13 (6 marks): Relative to a fixed origin O • the point A has position vector 4i − 3j + 5k • the point B has position vector 4j + 6k • the point C has position vector −16i + p
- November 2021, Pure 1, Q6 (5 marks): B C A Figure 1 Figure 1 shows a sketch of triangle ABC. Given that • AB → = −3i − 4j − 5k • BC → = i + j + 4k (a) find AC → (2) (b) show that cos ABC = 9 10 (3)
- November 2020, Pure 1, Q3 (4 marks): Relative to a fixed origin O ● point A has position vector 2i + 5j − 6k ● point B has position vector 3i − 3j − 4k ● point C has position vector 2i − 16j + 4k (
- June 2018, Pure 2, Q2 (5 marks): Relative to a fixed origin O, the point A has position vector (2i + 3j − 4k), the point B has position vector (4i − 2j + 3k), and the point C has position vecto
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