Simulation - Math
Drag vectors out of the box, drag back to remove.
The individual vectors can be changed by dragging.
The red arrow is the sum of all the vectors.
Drag to line up (tail of one arrow on the head of another) all the blue arrows to see if they always combine to give the red arrow.
Line them up in a different order to see if they still produce the same total (red) vector.
Write out each vector in component form (i.e. with $\hat i$ and $\hat j$) and add them up algebraically to see if it gives the same result.
Use the slider above to adjust the angle between the vectors.