plumiDistances and shortest distances: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on F.4 Distances and shortest distances, 2019–2025, 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 10 questions on Distances and shortest distances, as a list
- June 2025, Paper 2, Q11 (12 marks): The line L has vector equation = + − r 5 2 2 1 11 3 λ The point A has coordinates ( ) − − 1, 1, 6 11 (a) Find the coordi
- June 2025, AS Paper 1, Q10 (8 marks): The 3× 3 matrix M represents a reflection in the plane z = 0 The point A has position vector 2 5 4 The point A′ is the image of A under the reflection represent
- June 2024, Paper 1, Q12 (10 marks): The line L1 has equation r = 4 2 1 + λ 1 3 –1 The transformation T is represented by the matrix 2 1 0 3 4 6 –5 2 –3 The transformation T transforms the line L1
- June 2023, Paper 1, Q9 (9 marks): The position vectors of the points A, B and C are a = 2i + j + 2k b = −i − 8j + 2k c = −2j respectively. 9 (a) Find the area of the triangle ABC [4 marks] 9 (b)
- June 2022, Paper 1, Q10 (12 marks): In this question all measurements are in centimetres. A small, thin laser pen is set up with one end at A(7, 2, −3) and the other end at B(9, −3, −2) A laser be
- November 2021, Paper 1, Q11 (12 marks): The line L1 has equation r = 2 2 3 2 64 3 75 + l 2 3 −1 2 64 3 75 The line L2 has equation r = 6 4 1 2 64 3 75 + m −2 1 1 2 64 3 75 11 (a) Find the acute angle
- November 2020, Paper 1, Q11 (11 marks): The lines l1, l2 and l3 are defined as follows. l1 : r − 1 5 −1 2 664 3 775 0 B B @ 1 C C A × −2 1 −3 2 664 3 775 = 0 l2 : r − −3 2 7 2 664 3 775 0 B B @ 1 C C
- June 2019, Paper 1, Q10 (8 marks): The points A(5, −4, 6) and B(6, −6, 8) lie on the line L. The point C is (15, −5, 9). 10 (a) D is the point on L that is closest to C. Find the coordinates of D
- June 2019, Paper 2, Q7 (6 marks): The points A, B and C have coordinates A(4, 5, 2), B(−3, 2, −4) and C(2, 6, 1) 7 (a) Use a vector product to show that the area of triangle ABC is 5 11 p 2 [4 m
- June 2019, Paper 2, Q11 (8 marks): The line L1 has equation x − 2 3 = y + 4 8 = 4z − 5 5 The line L2 has equation r − −2 0 3 2 64 3 75 0 B @ 1 C A ≥ 2 1 3 2 64 3 75 = 0 Find the shortest distance
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