Addition of two vectors

We can also add two vectors together to get a new vector. If we think in terms of displacement vectors, we think of the sum of two vectors and (written ) as the following steps.

First, move from the origin along . Once you get to the end of the vector, start off in the direction of until you travel a distance equal to the length of . In the illustration, this total trip is exactly the same as if you had marched along the vector from the origin in the first place.

This is pretty intuitive. Think of a taking a trip. You start in Phoenix. The first leg of the trip takes you to Flagstaff. From there, you travel to Chicago. You could also get to the same final point (Chicago) by a direct flight from Phoenix and bypass Flagstaff completely.