I'm having troubles with constructing vectors. I understand and can apply the basics of vectors: dot products, null vector, unit vector, adding and subtracting vectors, scalar multiplication, etc... Which is fine and all, but when I'm faced with something relatively simple, like...

or

^When I see those types of questions, my head becomes confused. It's not that I don't know how to go about answering them, but more like, I can't get my head around how the vectors are constructed so I can't use/find the right numbers to find the vector (I hope that made sense).

I've searched around numerous sites/textbooks, but nothing that illuminates, or what I'm looking for... What I really want is a book/website that has a lot of questions and examples about the construction of these vectors (geometrically and algebraically), but that probably isn't going to happen.

Anyway, I'd love any sort of enlightenment on the construction of vectors, whether algebraically or geometrically! I'd appreciate any help!