plumiAngles with the scalar product: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 6.3 Angles with the scalar product, 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 Angles with the scalar product, as a list
- June 2025, Core Pure 2, Q2 (8 marks): An archer shoots an arrow towards a target. In a model • the arrow is a particle • the flight path of the arrow is a straight line • the target is part of a pla
- June 2025, AS Core Pure, Q10 (8 marks): The plane Π1 has equation x + y – z = 3 The plane Π2 has equation ax + 3y + 5z = 4 where a is an integer. Given that Π1 is perpendicular to Π2 (a) determine the
- June 2024, Core Pure 1, Q7 (10 marks): The line l1 has equation r = i – 2j + 3k + λ(2i + j – 4k) and the line l2 has equation r = 5i + pj – 7k + μ(6i + j + 8k) where λ and μ are scalar parameters and
- June 2024, Further Pure 1, Q9 (10 marks): (i) The line l1 has equation 2 3 3 4 1 1 r λ The line l2 has equation 13 1 5 2 8 5 r μ where λ and μ are scalar parameters. The li
- June 2024, AS Core Pure, Q6 (12 marks): The drainage system for a sports field consists of underground pipes. This situation is modelled with respect to a fixed origin O. According to the model, • the
- June 2023, AS Core Pure, Q6 (11 marks): The line l1 has equation 2 3 2 0 0 1 λ r where λ is a scalar parameter. The line l2 is parallel to 1 2 3 (a) Show that l1 and l
- June 2022, Core Pure 2, Q8 (13 marks): Two birds are flying towards their nest, which is in a tree. Relative to a fixed origin, the flight path of each bird is modelled by a straight line. In the mod
- June 2022, Further Pure 1, Q3 (9 marks): With respect to a fixed origin O, the points A and B have coordinates (2, 2, –1) and (4, 2p, 1) respectively, where p is a constant. For each of the following,
- June 2022, AS Core Pure, Q6 (13 marks): The surface of a horizontal tennis court is modelled as part of a horizontal plane, with the origin on the ground at the centre of the court, and • i and j are
- November 2020, Core Pure 1, Q4 (9 marks): The plane Π1 has equation r = 2i + 4j – k + λ (i + 2j – 3k) + μ(–i + 2j + k) where λ and μ are scalar parameters. (a) Find a Cartesian equation for Π1 (4) The l
- June 2019, Core Pure 1, Q7 (7 marks): The line lKDVHTXDWLRQ x y z − = + − = − 1 2 1 1 4 3 The line l2KDVHTXDWLRQ r = i + 3k + t(i − j + 2k where tLVDVFDODUSDUDPHWHU D 6KRZWKDWl an
- June 2018, AS Core Pure, Q4 (11 marks): Part of the mains water system for a housing estate consists of water pipes buried beneath the ground surface. The water pipes are modelled as straight line seg
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