How to Graph Vector Sums and Differences in GeoGebra

1.

Open Algebra View and Graphics View under  View in  Menu.

2.

Create three points $A$, $B$ and $C$.

3.

Use Vector  to make the vector from $A$ to $B$, the vector from $B$ to $C$, and the vector from $A$ to $C$.

You can see from the figure you have made that $\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}$. You can also see that $\overrightarrow{AC}-\overrightarrow{AB}=\overrightarrow{BC}$.