The important point to realize is this: vectors have both direction and magnitude. In your addition of vectors, you neglected the first of these facts (and one important fact about the addition of vectors that results as a consequence of the direction of vectors). Namely, you should always add from "head to tail".

If you call a vector

, you must realize that you are saying that the vector goes in the direction from point A to point F. Conversely, vector

goes in the exact opposite direction of

.

When you add vectors, the "head" of the first vector (the end point of that vector, which in the vector

would be F), must be connected to the "tail" of the second vector (the beginning point of that vector, which in the vector

would be D).

At this point, the resulting vector of the addition of these two goes from the tail of the first vector to the head of the second. In other words, in

, where

is congruent to, and therefore equal to,

, the tail of the first is A, the head of the second is E, and so: