wat if i still use it in the HSC and impress markers
I think it is going to be hard to penalise because some extension 2 texts use cross products despite it not being in the syllabus. They treat it as extension exercises. They don’t really go into it in much detail. Some IB texts have better and more thorough exercises on vectors including cross products, scalar triple products and their relation to coplanarity of vectors, minimum distance between skew lines using cross product and so on.
So exposure to this may mean some students will prefer to use quicker and more efficient methods in exams to save time, generally a good exam strategy.
The question posed in this thread however is a textbook question, not an exam question, so use of out-of-syllabus methods is OK.
If it were an exam question it might be more scaffolded to lead you into the longer method which I showed before.