harder GCSE vector questions

as far as I am aware these sorts of questions have only been posed by the Edexcel exam board in England (apologies if I've missed some from other boards)

they continue an erstwhile tradition - a general result seems to have been known to and used by Menelaus (~100CE, the logical one rather than the mythological one (maths rather than myths)) in his work on spherical geometry (but not involving vectors, obviously, because they were not invented until late in the 19th century)

a good focus on using vectors to prove (decent) results that can involve many variations of ratios

a powerpoint is here