plumiVector product: OCR A‑Level Further Maths questions
Every OCR A-Level Further Maths exam question on FP.11 Vector product, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Additional Pure Mathematics, question 2: The points P, Q, R and S have coordinates (1, 2, 4), (3, 1, 6), (4, 8, -2) and (5, 5, 5) respectively. (a) Find, in exact form, the area of triangle PQR. [3] (b](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54501-jun25-02-qp.webp?v=3)
![June 2019 Additional Pure Mathematics, question 6: K O K O K O 6 (a) For the vectors p 2 OO , q 1 OO and r 4 OO , calculate = = = - KK KK KK 3 1 5 - L P L P L P • p • q # r , • p # (q # r) , • (p # q) # r . [6]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54501-jun19-06-qp.webp?v=3)
All 9 questions on Vector product, as a list
- June 2025, Additional Pure Mathematics, Q2 (8 marks): The points P, Q, R and S have coordinates (1, 2, 4), (3, 1, 6), (4, 8, -2) and (5, 5, 5) respectively. (a) Find, in exact form, the area of triangle PQR. [3] (b
- June 2024, AS Additional Pure Mathematics, Q2 (6 marks): The points A and B have position vectors a and b relative to the origin O. It is given that J N J N 2 m K O K O a 4 and b 4 OO , where m is a real parameter. =
- June 2022, Additional Pure Mathematics, Q5 (8 marks): You are given the variable point A(3, −8, t), where t is a real parameter, and the fixed point B(1, 2, −2). (a) Using only the geometrical properties of the vec
- June 2022, AS Additional Pure Mathematics, Q1 (6 marks): K O K O K O 1 The points A, B and C have position vectors a 1 OO, b 3 OO and c 1 OO respectively, = KK = KK = KK 3 1 2 - L P L P L P relative to the origin O. (
- November 2021, Additional Pure Mathematics, Q3 (6 marks): The points P, Q and R have position vectors p 2 i j 5 k , q = - + and i j k r 2 i j t k = + + = + + respectively, relative to the origin O. Determine the value(
- November 2021, AS Additional Pure Mathematics, Q1 (5 marks): K O K O K O 1 The points A, B and C have position vectors a 0 OO , b 4 OO and c 0 OO respectively, relative to = KK = KK = KK 0 0 1 L P L P L P the origin O. (a
- November 2020, AS Additional Pure Mathematics, Q6 (9 marks): The points A and B have position vectors a i 2 j + and b k i3 4 j 5 k respectively. = + =- + - (a) Determine the area of triangle OAB, giving your answer in an
- June 2019, Additional Pure Mathematics, Q6 (12 marks): K O K O K O 6 (a) For the vectors p 2 OO , q 1 OO and r 4 OO , calculate = = = - KK KK KK 3 1 5 - L P L P L P • p • q # r , • p # (q # r) , • (p # q) # r . [6]
- June 2019, AS Additional Pure Mathematics, Q5 (8 marks): The tetrahedron T, shown below, has vertices at O(0, 0, 0), A(1, 2, 2), B(2, 1, 2) and C(2, 2, 1). C Diagram not drawn to scale B O A ^ h 1 Show that the surfac
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