plumiDistances and shortest distances: OCR MEI A‑Level Further Maths questions
OCR MEI 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 7 questions on Distances and shortest distances, as a list
- June 2025, Core Pure, Q11 (14 marks): The lines l1 and l2 have equations y 1 x z 3 + 2 - - l1: l2: r 2 i j 3 k ( i cj 2 k ) = = = + + + m - + + a b 1 where a, b and c are constants. (a) In the case
- June 2024, Core Pure, Q11 (14 marks): The plane P has equation x 2 y 2 z 4 . The point P has coordinates (8, 4, 5). - + = (a) Calculate the shortest distance from P to P. [2] The line L has equation
- June 2023, Core Pure, Q16 (10 marks): and the line x 3 y 1 z + , 5 - - 16 The point P (4, 1, 0) is equidistant from the plane x 2 y 2 z 0 + + = = = 2 b 3 where b 2 0 . Determine the value of b. [10]
- June 2022, Core Pure, Q13 (17 marks): The points A and B have coordinates (4, 0, -1) and (10, 4, -3) respectively. The planes P and 1 P have equations x y = and x y z 2 5 2 3 - = - respectively. 4 -
- November 2021, Core Pure, Q11 (9 marks): (a) Given that u = mi + j - 3k and v = i + 2j - 2k, find the following, giving your answers in terms of m. (i) u.v [1] (ii) u #v [2] (b) Hence determine (i) the
- November 2020, Core Pure, Q15 (17 marks): (a) Show that the three planes with equations x y z 3 12 + m + = - x y z 2 5 11 + + = - x y z 2 2 9 - + = - where m is a constant, meet at a unique point except
- November 2020, Extra Pure, Q6 (17 marks): 4 2 2 6 A surface S is defined by z f ( , ) x y 4 x 4 y 17 x y . = = + - (a) (i) Show that there is only one stationary point on S. [5] The value of z at the st
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