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Vectors: OCR MEI A‑Level Maths questions

Every OCR MEI A-Level Maths exam question on P.10 Vectors, 2018–2025, with its mark scheme and examiner’s report.

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560 questions

  1. Q9

    June 2025 · Paper 2

    3 marksP.10 Vectors
    The whole paper ↗
    June 2025 Paper 2, question 9: K O K O 9 The position vectors of the points A and B are OA 2 OO and OB 1 OO respectively. = KK - = KK 0 3 - L P L P (a) Write down the vector AB. [1] The point

  2. Q10

    June 2025 · Paper 3

    6 marksP.10 VectorsP.2 Algebra and functions
    The whole paper ↗
    June 2025 Paper 3, question 10: KKKKKKK OOOOOOO 10 The magnitude of the vector 1 is an integer. - x L P Determine all possible integer values of x. [6]

  3. Q7

    June 2025 · AS Paper 1

    5 marksP.10 Vectors
    The whole paper ↗
    June 2025 AS Paper 1, question 7: c m. a k. The vector AB is 6 – 2 8 7 The point A has position vector 1 (a) On the axes in your Printed Answer Book, draw the position of the points A and B. [2]

  4. Q4

    June 2024 · Paper 1

    4 marksP.10 Vectors
    The whole paper ↗
    June 2024 Paper 1, question 4: The vectors v1 and v2 are defined by v1 = 2 a i b j and v2 b i 3 j where a and b are constants. + = - Given that 3 v v 22 i 9 j , find the values of a and b. [4

  5. Q5

    June 2023 · Paper 2

    3 marksP.10 Vectors
    The whole paper ↗
    June 2023 Paper 2, question 5: J N J N 3 5 KK OO and OB KK OO . 5 You are given that OA = - = - 1 3 L P L P Determine the exact length of AB. [3]

  6. Q6

    June 2023 · Paper 3

    10 marksP.10 VectorsP.3 Coordinate geometry
    The whole paper ↗
    June 2023 Paper 3, question 6: (a) Quadrilateral KLMN has vertices K ( - , 1), L (5, 1 4 - ), M (6, 2) and N (2, 5), as shown in Fig. 6.1. Fig. 6.1 y N (2, 5) R S M (6, 2) K (−4, 1) Q x O P L

  7. Q3

    June 2023 · AS Paper 1

    4 marksP.10 Vectors
    The whole paper ↗
    June 2023 AS Paper 1, question 3: p and 5 f 2 f p respectively. The vector AC is f 2 p. - 3 The points A and B have position vectors 1 2 4 - (a) Write down the position vector of C as a column v

  8. Q4

    June 2022 · AS Paper 2

    4 marksP.10 Vectors
    The whole paper ↗
    June 2022 AS Paper 2, question 4: = c m and the position vector of Q is q = c m. 4 28 4 The position vector of P is p 3 10 (a) Determine the magnitude of PQ. [2] (b) Determine the angle between

  9. Q6

    November 2021 · Paper 2

    5 marksP.10 Vectors
    The whole paper ↗
    November 2021 Paper 2, question 6: You are given that v 2 a 3b , where a and b are the position vectors = + = c m and b 5 c 1 m . = - a 3 6 (a) Determine the magnitude of v. [3] (b) Determine the

  10. Q8

    November 2021 · AS Paper 2

    4 marksP.10 Vectors
    The whole paper ↗
    November 2021 AS Paper 2, question 8: With respect to an origin O, the position vectors of the points A and B are c m c m 3 6 = - OA and OB . = 20 8 (a) Determine whether AB 2 200 . [2] a k. 18 The

  11. Q3

    November 2020 · Paper 1

    3 marksP.10 Vectors
    The whole paper ↗
    November 2020 Paper 1, question 3: K O K O 3 The points A and B have position vectors a 2 OO and b = 4 OO respectively. = KK KK 1 8 - L P L P Show that the exact value of the distance AB is 101.

  12. Q4

    November 2020 · Paper 3

    3 marksP.10 Vectors
    The whole paper ↗
    November 2020 Paper 3, question 4: Fig. 4 shows the regular octagon ABCDEFGH. F E G D H C A B Fig. 4 i CD = , where i is a unit vector parallel to the x-axis and j is a unit vector parallel to th

  13. Q3

    November 2020 · AS Paper 1

    5 marksP.10 Vectors
    The whole paper ↗
    November 2020 AS Paper 1, question 3: Fig. 3 shows a triangle PQR. The vector PQ is i+ 7j and the vector QR is 4i- 12j. Q P R Fig. 3 (a) Show that the triangle PQR is isosceles. [3] The point P has

  14. Q10

    June 2018 · Paper 3

    10 marksP.10 VectorsP.2 Algebra and functions
    The whole paper ↗
    June 2018 Paper 3, question 10: f p where a and b can vary, point B has position vector f p and point C has 10 b Point A has position vector 2 0 0 2 f p. ABC is an isosceles triangle with AC =
All 14 questions on Vectors, as a list
  1. June 2025, Paper 2, Q9 (3 marks): K O K O 9 The position vectors of the points A and B are OA 2 OO and OB 1 OO respectively. = KK - = KK 0 3 - L P L P (a) Write down the vector AB. [1] The point
  2. June 2025, Paper 3, Q10 (6 marks): KKKKKKK OOOOOOO 10 The magnitude of the vector 1 is an integer. - x L P Determine all possible integer values of x. [6]
  3. June 2025, AS Paper 1, Q7 (5 marks): c m. a k. The vector AB is 6 – 2 8 7 The point A has position vector 1 (a) On the axes in your Printed Answer Book, draw the position of the points A and B. [2]
  4. June 2024, Paper 1, Q4 (4 marks): The vectors v1 and v2 are defined by v1 = 2 a i b j and v2 b i 3 j where a and b are constants. + = - Given that 3 v v 22 i 9 j , find the values of a and b. [4
  5. June 2023, Paper 2, Q5 (3 marks): J N J N 3 5 KK OO and OB KK OO . 5 You are given that OA = - = - 1 3 L P L P Determine the exact length of AB. [3]
  6. June 2023, Paper 3, Q6 (10 marks): (a) Quadrilateral KLMN has vertices K ( - , 1), L (5, 1 4 - ), M (6, 2) and N (2, 5), as shown in Fig. 6.1. Fig. 6.1 y N (2, 5) R S M (6, 2) K (−4, 1) Q x O P L
  7. June 2023, AS Paper 1, Q3 (4 marks): p and 5 f 2 f p respectively. The vector AC is f 2 p. - 3 The points A and B have position vectors 1 2 4 - (a) Write down the position vector of C as a column v
  8. June 2022, AS Paper 2, Q4 (4 marks): = c m and the position vector of Q is q = c m. 4 28 4 The position vector of P is p 3 10 (a) Determine the magnitude of PQ. [2] (b) Determine the angle between
  9. November 2021, Paper 2, Q6 (5 marks): You are given that v 2 a 3b , where a and b are the position vectors = + = c m and b 5 c 1 m . = - a 3 6 (a) Determine the magnitude of v. [3] (b) Determine the
  10. November 2021, AS Paper 2, Q8 (4 marks): With respect to an origin O, the position vectors of the points A and B are c m c m 3 6 = - OA and OB . = 20 8 (a) Determine whether AB 2 200 . [2] a k. 18 The
  11. November 2020, Paper 1, Q3 (3 marks): K O K O 3 The points A and B have position vectors a 2 OO and b = 4 OO respectively. = KK KK 1 8 - L P L P Show that the exact value of the distance AB is 101.
  12. November 2020, Paper 3, Q4 (3 marks): Fig. 4 shows the regular octagon ABCDEFGH. F E G D H C A B Fig. 4 i CD = , where i is a unit vector parallel to the x-axis and j is a unit vector parallel to th
  13. November 2020, AS Paper 1, Q3 (5 marks): Fig. 3 shows a triangle PQR. The vector PQ is i+ 7j and the vector QR is 4i- 12j. Q P R Fig. 3 (a) Show that the triangle PQR is isosceles. [3] The point P has
  14. June 2018, Paper 3, Q10 (10 marks): f p where a and b can vary, point B has position vector f p and point C has 10 b Point A has position vector 2 0 0 2 f p. ABC is an isosceles triangle with AC =

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