plumiThe vector product: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 11.1 The vector product, 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 22 questions on The vector product, as a list
- June 2025, Pure Core 2, Q1 (3 marks): In this question you must show detailed reasoning. J N J N 2 1 - K O K O Vectors a and b are given by a 4 OO and b 3 OO. = - KK = KK 3 2 - L P L P Determine, in
- June 2025, AS Pure Core, Q2 (5 marks): K O K O 2 Two vectors, a and b, are given by a O where p is a constant. 3 OO and b 6 K O = - KK = K 13 p L P L P (a) Find expressions in terms of p for each of
- June 2025, AS Additional Pure Mathematics, Q2 (6 marks): K O K O K O 2 The vectors p, q and r are such that p 3 , q 4 OO and r 1 OO. = KK OO = - KK = KK 7 9 2 - L P L P L P (a) (i) Determine the value of the integer k
- June 2024, Pure Core 2, Q5 (6 marks): Vectors, a, b and c, are given by a i ( 1 p ) j ( p 2 ) , k b 2 i j k and = + - + + = + + c i 14 j ( p 3 ) k where p is a constant. = + + - You are given that a
- June 2024, Additional Pure Mathematics, Q4 (10 marks): K O K O 4 The vectors a and b are given by a q 2 OO and b 2 q 5 OO, where p, q and r are real numbers. = KK + = KK - 2 r 3 r 3 - + L P L P (a) Given that b is n
- June 2024, AS Pure Core, Q3 (7 marks): K O K O 3 (a) (i) Find 2 5 OO. [1] KK OO KK # 1 2 - - L P L P (ii) State a geometrical relationship between the answer to part (a)(i) and the J N J N 1 3 K O K
- 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 2023, Additional Pure Mathematics, Q3 (7 marks): The points A and B have position vectors a i p j q k and b 2 i 3 j 2 k respectively, = + + = + + relative to the origin O. (a) Determine the value of p and the
- June 2023, AS Pure Core, Q2 (8 marks): The lines L1 and L2 have the following equations. J N J N 5 5 - K O K O L : r 6 2 = + - KK OO m KK OO 1 15 2 - L P L P J N J N 24 3 K O K O L : r 1 1 = + KK OO
- June 2022, Pure Core 2, Q1 (6 marks): (a) Find a vector which is perpendicular to both 3i - 5j - k and i + 3j - 4k. [1] The equations of two lines are r = 2i + 3j + 3k+ m(i - 2j + k) and r = i + 11j
- 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 Pure Core, Q1 (8 marks): K O K O 1 (a) Determine whether the point (19, -12, 17) lies on the line r 2 2 OO. [3] = - KK OO + m KK - 7 4 L P L P J N J N 1 3 - K O K O Vectors a and b are
- 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, Pure Core 1, Q6 (5 marks): The equations of two non-intersecting lines, l1 and , l2 are J N J N J N J N 1 2 2 1 K O K O K O K O l : r 2 1 OO , l : r 2 1 . = KK OO + m KK = KK OO + n KK -
- November 2020, Additional Pure Mathematics, Q4 (7 marks): Points A, B and C have position vectors a, b and c respectively, relative to origin O. It is given that b c a and that a = . 3 = # (a) Determine each of the fol
- November 2020, AS Pure Core, Q7 (6 marks): The equations of two intersecting lines are J N J N J N J N 12 2 2 3 - - K O K O K O K O r = a 2 OO r = 0 1 + + KK OO m KK KK OO n KK OO 1 1 5 1 - - L P L P L P
- 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 Pure Core, Q3 (10 marks): The position vector of point A is a 9 i 2 j 6 k . =- + + The line l passes through A and is perpendicular to a. (a) Determine the shortest distance between the
- June 2019, AS Additional Pure Mathematics, Q3 (4 marks): The non-zero vectors x and y are such that x # y = 0. (a) Explain the geometrical significance of this statement. [2] (b) Use your answer to part (a) to explain
- June 2018, AS Pure Core, Q1 (5 marks): f p and f p. 1 (i) Find a vector which is perpendicular to both [2] 3 6 - 2 4 - (ii) The cartesian equation of a line is x y z 3 2 + . 4 = - = 2 [3] Express the
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