How do the components of a vector transform under a translation of coordinates?

Vectors are invariant under translation. This means that they are unaffected or unchanged even if the coordinates are translated. So while the coordinates of two points are changed or moved during translation, the distance between the two points does not change. The best way to picture this out is using real life scenario. For example, you and I are at rest relative to each other but sitting on a plane at different locations, then we will have a fixed distance. Now the plane flies and its overall location is changed, similarly our individual coordinates also change but the distance between us will remain the same.