plumiVectors in two dimensions: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.10.1 Vectors in two dimensions, 2018–2025, 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 14 questions on Vectors in two dimensions, 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, 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, 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, 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, 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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