Say we have three forces $F_1, F_2, F_3$, such that
$$ F_1 + F_2 - F_3 = 0\hspace 10mm (1) $$
And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the magnitude of either, in the opposite direction.
From this it would seem that $F_1$ and $F_2$ had the same direction (in highschool physics, at least!), but if we treat these vectors like numbers, we can make another statement:
$$ F_1 - F_3 = - F_2\hspace 10mm (2) $$
And yet this seems absurd to me, since equality of vectors seems to imply equality of direction. From the statement in $(1)$ I can also state that: $$ F_1 = F_2\hspace 10mm (3) $$
But this contradicts $(2)$!
Edit: So they don't contradict, but I guess what I was wondering was the notation -- that is, if we say that there is a force $F = ma$, $F - ma = 0$ follows. Does this mean that $ma$ and $F$ are in opposite directions? What does the negative sign really mean?
I'm sure I've probably totally missed the point of vectors, but I can't seem to be able to contract this question into a Google search.