I would like to know whether I am correct in my thinking below.

You can add two vectors using basic arithmetic only when either two cases occur:

(1) the vectors are parallel to each other

(2) the vectors direction are opposite of each other (in which case, you could multiply one of the vectors by -1 in order to make them be parallel to each other, and then (1) would apply).

Otherwise, you would have to use those fancy triangle laws and follow tip-to-tail methods etc.

Is this correct? Please help!