plumiVectors: OCR A‑Level Maths questions
Every OCR A-Level Maths exam question on P.10 Vectors, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 1, question 4: The position vector of the point A is . 0 5 i 0 5 . j . - (a) Determine whether . 0 5 i 0 5 . j is a unit vector. [2] - (b) Find the direction of . 0 5 i 0 5 .](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-04-qp.webp?v=3)
![June 2024 Paper 2, question 2: J N The vector a KK OO has magnitude 6 and direction 60° above the positive x-axis. 2 b L P Determine the exact values of a and b. [4]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun24-02-qp.webp?v=3)
![June 2023 Paper 1, question 4: It is given that ABCD is a quadrilateral. The position vector of A is i j + , and the position vector of B is i j 3 5 . + (a) Find the length AB. [1] (b) The po](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun23-04-qp.webp?v=3)
![June 2023 AS Paper 1, question 2: c 4 m, c 3 m and c 1 m respectively. - - - 2 (a) The points A, B and C have position vectors 3 6 12 (i) Show that B lies on AC. [2] (ii) Find the ratio AB BC .](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-jun23-02-qp.webp?v=3)
![June 2022 Paper 2, question 2: The points A and B have position vectors i 3 2 j and i 4 2 j 5 k respectively. + + - (a) Find the length of AB. [2] Point P has position vector i p 3 k , where](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun22-02-qp.webp?v=3)
![June 2022 AS Paper 2, question 7: A 2i + 4j C O 4i – 3j B The diagram shows the parallelogram OACB where OA 2 i 4 j and OB 4 i 3 j . = + = - 2 5 (a) Show that cos AOB . [5] = - 25 (b) Hence find](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23002-jun22-07-qp.webp?v=3)
![November 2021 AS Paper 1, question 4: c m c m. 6 1 - 4 (a) Simplify 2 3 [2] - 3 2 - c m c m, where r and s are constants. 6 1 - (b) The vector a is defined by a r s = + 3 2 - Determine two pairs of](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-nov21-04-qp.webp?v=3)
![June 2018 Paper 2, question 2: K O K O 2 The points A and B have position vectors 2 OO and 1 OO respectively. KK - KK - 5 2 L P L P (i) Find the exact length of AB. [2] (ii) Find the position](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun18-02-qp.webp?v=3)
All 18 questions on Vectors, as a list
- June 2025, Paper 1, Q4 (7 marks): The position vector of the point A is . 0 5 i 0 5 . j . - (a) Determine whether . 0 5 i 0 5 . j is a unit vector. [2] - (b) Find the direction of . 0 5 i 0 5 .
- June 2025, AS Paper 1, Q7 (7 marks): In this question you must show detailed reasoning. B C P c Q A a O The diagram shows a parallelogram OABC. The position vectors of A and C are a and c respectiv
- June 2024, Paper 2, Q2 (4 marks): J N The vector a KK OO has magnitude 6 and direction 60° above the positive x-axis. 2 b L P Determine the exact values of a and b. [4]
- June 2024, AS Paper 1, Q2 (6 marks): Points A and B have position vectors OA 2 i 3 j and OB i 5 j , respectively, where O is the = + =- + origin. (a) Find the position vector of the midpoint of AB.
- June 2023, Paper 1, Q4 (8 marks): It is given that ABCD is a quadrilateral. The position vector of A is i j + , and the position vector of B is i j 3 5 . + (a) Find the length AB. [1] (b) The po
- June 2023, Paper 2, Q2 (5 marks): K O K O 2 The points O and A have position vectors 0 OO and 0 OO respectively. The point P is such that KK KK 0 8 L P L P OP k OA , where k is a non-zero consta
- June 2023, AS Paper 1, Q2 (8 marks): c 4 m, c 3 m and c 1 m respectively. - - - 2 (a) The points A, B and C have position vectors 3 6 12 (i) Show that B lies on AC. [2] (ii) Find the ratio AB BC .
- June 2022, Paper 2, Q2 (5 marks): The points A and B have position vectors i 3 2 j and i 4 2 j 5 k respectively. + + - (a) Find the length of AB. [2] Point P has position vector i p 3 k , where
- June 2022, AS Paper 2, Q7 (9 marks): A 2i + 4j C O 4i – 3j B The diagram shows the parallelogram OACB where OA 2 i 4 j and OB 4 i 3 j . = + = - 2 5 (a) Show that cos AOB . [5] = - 25 (b) Hence find
- November 2021, Paper 2, Q9 (6 marks): Points A, B and C have position vectors a, b and c relative to an origin O in 3-dimensional space. Rectangles OADC and BEFG are the base and top surface of a cu
- November 2021, AS Paper 1, Q4 (7 marks): c m c m. 6 1 - 4 (a) Simplify 2 3 [2] - 3 2 - c m c m, where r and s are constants. 6 1 - (b) The vector a is defined by a r s = + 3 2 - Determine two pairs of
- November 2020, Paper 1, Q5 (8 marks): B b O A a The diagram shows points A and B, which have position vectors a and b with respect to an origin O. P is the point on OB such that OP : PB = 3:1 and Q
- November 2020, Paper 2, Q7 (8 marks): A and B are fixed points in the x-y plane. The position vectors of A and B are a and b respectively. State, with reference to points A and B, the geometrical si
- November 2020, AS Paper 1, Q2 (5 marks): J N J N 3 OO and 1 - KK KK OO respectively. 2 Points A and B have position vectors 4 2 L P L P J N Point C has position vector p KK OO and ABC is a straight lin
- June 2019, Paper 1, Q2 (8 marks): The point A is such that the magnitude of OA is 8 and the direction of OA is 240°. (a) (i) Show the point A on the axes provided in the Printed Answer Booklet.
- June 2019, AS Paper 2, Q5 (6 marks): c m, b = 3 c m, c = 7 c m and d = k c m. Points A, B, C and D have position vectors a = 1 4 5 2 5 4 (a) Find the value of k for which D is the midpoint of AC. [
- June 2018, Paper 2, Q2 (6 marks): K O K O 2 The points A and B have position vectors 2 OO and 1 OO respectively. KK - KK - 5 2 L P L P (i) Find the exact length of AB. [2] (ii) Find the position
- June 2018, AS Paper 1, Q7 (7 marks): OABC is a parallelogram with OA= a and OC = c. P is the midpoint of AC. A B a P O c C (i) Find the following in terms of a and c, simplifying your answers. (a)
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