Preposition διὰ (“Dia”)

v. 3 – DIA with the GENITIVE: διὰ τῆς σαρκός
The powerlessness of the law in which it was weak through the agency of the flesh
v. 11 – through the agency of the indwelling his own (the very) spirit in  you
v. 21 – through the agency of the one subjecting it (creation)

• law is weak through the agency of the flesh
• body is resurrected through the agency of the indwelling spirit
• creation subjected to vanity through the agency of the one subjecting it

v. 10 – DIA with the ACCUSATIVE: τὸ μὲν σῶμα νεκρὸν διὰ ἁμαρτίαν

• The indeed body dead because of sin
• The and spirit life because of righteousness

dia (Genitive, Accusative)

1. With Genitive
a. Agency: by, through
b. Means: through
c. Spatial: through
d. Temporal: through(out), during
2. With Accusative
a. Cause: because of, on account of, for the sake of
b. Spatial (rare): through