Hi, have a look at the attached diagrams:
earboth, according to your diagram, isn't a + BC = d or OD? not AD as you have it written?
since AD || BC, and since its a parallelogram, shouldnt AD = BC? so why is AD = a + BC? Im thinking a + BC yields the vector from the origin to D, OD.
EDIT: i see [.math] notation is back.