plumiLines and planes in 3-D: WJEC A‑Level Further Maths questions
Every WJEC A-Level Further Maths exam question on 1.5 Lines and planes in 3-D, 2018–2025, with its mark scheme and examiner’s report.
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All 8 questions on Lines and planes in 3-D, as a list
- Summer 2025, AS Unit 1, Q2 (14 marks): 2. Three points, A, B, C, are such that A(3, 2, 5), B(4, 0, 1), and C(–3, 2, 0). The line L1 passes through the points A and B, and the line L2 passes through t
- Summer 2024, AS Unit 1, Q9 (8 marks): and , are defined by 9. Two planes, 1 2 1 : 4 x 3 y 2 z 5 , 2 :6 9 x y z . and . Give your answer correct to three (a) Find the acute angl
- Summer 2023, AS Unit 1, Q5 (6 marks): 5. The points A and B have coordinates (3, 4, –2) and (–2, 0, 7) respectively. The equation of the plane ∏ is given by 2x + 3y + 3z = 27. (a) Show that the vect
- Summer 2022, AS Unit 1, Q3 (5 marks): 3. The vector equation of the line L is given by r = –i + 2j – 6k + λ (4i – 2j + 7k). The Cartesian equation of the plane ∏ is given by 3x + 8y – 9z = 0. Find t
- Summer 2022, AS Unit 1, Q7 (7 marks): 7. The vector equations of the lines L1, L2, L3 are given by r = 3i + 2j + k + λ (2i + nj + k), r = 5i – 3j – 4k + μ (3i + j – 3k), r = 6i – 3j + 2k + v (pi + 3
- Summer 2019, AS Unit 1, Q2 (7 marks): The position vectors of the points A, B, C, D are given by 2. a = 2i + 3j – k, b = 4j + 5k, c = 7i – 3k, d = –3i – j – 5k, respectively. Find the vector equatio
- Summer 2019, AS Unit 1, Q8 (9 marks): 8. The plane Π contains the three points A(3, 5, 6), B(5, –1, 7) and C(–1, 7, 0). Find the vector equation of the plane Π in the form r.n = d. Express this equa
- Summer 2018, AS Unit 1, Q9 (14 marks): 9. The line L1 passes through the points A(1, 2, –3) and B(–2, 1, 0). (a) (i) Show that the vector equation of L1 can be written as r = (1 – 3λ)i + (2 – λ)j + (
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