Geometric consequence of absolute vectors

Let's see what $a+b$ is, geometrically. The dark blue arrows are $a$ and $b$. The orange vector is $a+b$.

Essentially, you just stick one on top of the other. Now, we know that the absolute value of a vector just represents the length; can you see what happens when $|a+b|=|a|+|b|$?

Essentially, they would have to be pointing in the same direction! It has nothing to do with what quadrant they're in, it only says they're the same direction. The converse is also true; if $a$ and $b$ point in the same direction, then $|a+b|=|a|+|b|$ (do you see why?).