Technically, every vector \mathbf{r} (the r standing for “radius” from the arbitrarily chosen origin) should be written in terms of basis vectors, e.g. \mathbf{\hat{x}}, like so:


But in reality everybody knows about the basis vectors, and then can be assumed. You can write the same vector by omitting them — so long as you realize, conceptually, that they are implicit in the formula: