I think A-levels are the equivalent of the final year of High School (English High School finishes when you are 16, then AS & A-levels carry on until you are 18... it's all pretty complicated).
Anyway, I know somebody whos finished A-level mathematics, and he told me that my example was actually a fairly simple vector question, so he gave me a harder one.
Now that one isn't even in English. >.<The points A and B have position vectors 2i + 3j and i + j respectively, relative to the origin O. The point P lies on OA produced and is such that OP = 2OA; Q lies on OB produced and is such that OQ = 3OB. Find the vector equations of the lines AQ and BP and find also the position vector of the point of intersection of these two lines.
The point Z has position vector k relative to O. Show that the cosine of the acute angle between ZA and ZB is /(6/7) and find the area of the triangle ZAB giving your answer in surd form.