Consider the next example. Standing back on your coordinate axis, you daringly decide to venture out, but not along any coordinate axis. First you walk roughly the same displacement as the last problem, to the point [4,3]. Next you continue on, 3m to the east and 4m to the north. Lastly, you take a few steps backwards, traveling 3m west and 1m north. What is your final location? We can see some illustration of this in the picture above. Each walk is shown in color, while the entire traversed distance is shown in black. Following the steps from before, each motion is laid from tip to tail, and the final displacement vector is drawn from the tail of the first vector to the tip of the final. If you had graph paper and performed this to scale, you could have an exact answer without having to do any sort of mathematics. The math side of things, we can simply add d1 to d2, and then add d3 to get our final vector.
So, ultimately, on your little stroll, you walked 4m to the east, and 8m to the north. One thing that is incredibly illustrative about this example, but a little confusing is that in the walking example, the walker always ends at the same point that the next vector starts. In a physics problem, if you are given vectors in this way, and they are all centered around the origin, say in the case of a force problem, several forces are all acting on a single body at the origin, you can still add them in this way, because remember it is possible to slide vectors any which way, and as long as the magnitude and direction stays intact, the vector remains intact, so it is always possible to line them all tip to tail in this way, in any order, and get your resultant vector.
