plumiDistances and shortest distances: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 6.4 Distances and shortest distances, 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 12 questions on Distances and shortest distances, as a list
- June 2025, Pure Core 1, Q7 (8 marks): A 3-D coordinate system, whose units are metres, is set up to model a street containing telephone cables T1 and T2. The cables are modelled as straight lines wi
- June 2024, Pure Core 1, Q11 (7 marks): A 3-D coordinate system, whose units are metres, is set up to model a construction site. The construction site contains four vertical poles P1, P2, P3 and P4. T
- June 2024, AS Pure Core, Q5 (10 marks): The line through points A 8 ( , 7 , 2 ) and B 11 ( , 9 0 , ) is denoted by L1. - - - (a) Find a vector equation for L1. [2] (b) Determine whether the point ( 26
- June 2023, Pure Core 1, Q8 (15 marks): The points P, Q and R have coordinates (0, 2, 3), (2, 0, 1) and (1, 3, 0) respectively. The acute angle between the line segments PQ and PR is i. 2 (a) Show tha
- June 2023, Pure Core 2, Q6 (8 marks): K O K O K O 6 The equation of the plane % is r 2 4 3 OO. = + + KK OO m KK OO n KK 1 3 1 L P L P L P J N 2 K O (a) Find the acute angle between % and the plane w
- June 2022, Pure Core 2, Q10 (8 marks): The coordinates of the points A and B are (3, -2, -1) and (13, 10, 9) respectively. • The plane %A contains A and the plane %B contains B. • The planes %A and %
- November 2021, Pure Core 1, Q4 (11 marks): Points A, B and C have coordinates (4, 2, 0), (1, 5, 3) and (1, 4, -2) respectively. The line l passes through A and B. (a) Find a cartesian equation for l. [3]
- 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 -
- June 2019, Pure Core 1, Q8 (6 marks): The equation of a plane is x 4 2 y z 7 . + + = The point A has coordinates (9, 6, 1) and the point B is the reflection of A in the plane. Find the coordinates o
- June 2019, Pure Core 2, Q2 (8 marks): K O 2 (a) A plane P has the equation r. 6 15 . C is the point (4, -5, 1). KK OO = 2 - L P Find the shortest distance between P and C. [3] (b) Lines l1 and l2 ha
- 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, Q8 (13 marks): The motion of two remote controlled helicopters P and Q is modelled as two points moving along straight lines. J N J N p q 2 4 5 8 + + K O K O Helicopter P move
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