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When a particle moves from [tex]r_{1}[/tex] to [tex]r_{2}[/tex], the amplitude of the move can be written as:

[tex]\langle r_{2} | r_{1} \rangle = \frac{e^{ipr_{12}/\hbar}}{r_{12}}[/tex]

where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are vectors of particle's position (I think?).

and [tex]r_{12} = r_{2}-r_{1}[/tex] and is the scalar( I think again?)

So my question is.. how can you substitute vectors to get a numerical value for the equation above?