More generally, we can define a displacement vector. These vectors are very similar to position vectors, but instead of being a directed line segment from the origin to a point, they are directed line segments between any two coordinate points. The picture below shows a displacement vector from the point (-1,2) to the point (5,-5).
This vector could be written as (5-(-1), 2-5) = (6,-3) since it starts at the point (-1,2) and moves three units to the right and five units up to get to the point (5,5). Notice that the position vector from the origin to the point (6,-3) looks exactly the same as this vector, but is placed in a different location. Two vectors are said to be equal if they have the same direction and magnitude. In this case, both vectors have a length of sqare root [(6)2 + (-3)2] = 3 square root[5] and point in the same direction. Thus, they are the same vector. Their location is irrelevant.