In a text I found the following:
Assume that the two (non-zero) vectors u, v are linearly dependent. This means that one can be written as a linear combination of the other; so, $\mathbf{u} =\alpha\mathbf{v}$. So for two vectors, linear dependence means that they point into the same, or opposite direction; that is they lie on the same line through $\mathbf{O}$.
My confusion is the part where it states that the vectors lie along the line that "goes through $\mathbf{O}$". The only explanation I could come up with was that, they should be position vectors (and thus already on a line to begin with)
Is my assumption correct; or could elements of real vector space be more similar to displacement vectors with a tail that's positioned at a point other than the origin?
Considering displacement vectors, instead of vectors with tail in the origin, gives origin to the structure of Affine space. $\mathbb{R}^n$ can be seen both as a vector space and as an affine space (as in general every vector space is an affine space too)