Any account of Dirac's bra-ket vectors depends critically on your understanding of vector spaces. Unfortunately, we have no idea as to how familiar you are with such concepts and cannot take on the task of educating you in vector spaces. I suggest you look at the Wikipedia article at https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation
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Two vectors: no. Three vectors: yes.
Two vectors, no; three vectors yes.
Yes.
Assuming you want non-zero vectors, two opposing vectors will give a resultant of zero.
In vector addition, the sum of two (or more) vectors will give a resultant vector. There are a number of sites that will help you with tutorials. A link to one can be found below.