I'm trying to learn vectors but I can't find a decent book which explains vectors in depth.
I need a book which explains vectors from the beginning, using a beginner's approach(assuming the reader never knew about vectors before, this may be exaggerated so, it's not a problem if it assumes you know high school vectors, which I know).
I'm looking to learn about dot/cross products, laws of sines/cosines, theorems, proofs involving vectors, stuff like "Prove that we are not at the center of the universe", etc.
Could you please recommend some books for these.
Thanks.