κατὰ, ἐν, εἰς
In our introductory message to 1 Peter, we observed in 1:2 that the Trinity shows up. Specifically, the readers of Peter's letter were elect and living as foreigners by something specific each member of the Trinity did:
according to the foreknowledge of God the Father,
by the sanctifying work of the Spirit,
for obedience and sprinkling with the blood of Jesus Christ
The Trinity (Father, Son, and Holy Spirit; one God existing eternally in three Persons) is one of the harder aspects of Christian theology to know what to do with. We can use simple words to describe it ("one God, three Persons"), but what does that actually mean?
Perhaps you've seen illustrations and analogies trying to explain the Trinity. I can almost guarantee you whatever illustrations you've seen are woefully inadequate in some critical way.
And that's just the theology of it. What about where my daily life comes in? How does the reality of the Trinity actually matter in my life? What difference does it make? Because if I get that, then I'm not so bothered that I don't fully comprehend the theological constructs.
This passage helps a bit, because each member of the Trinity does something unique. What each One does gives us a clue how He relates to us. But more than tasks, each one in this verse has a preposition different than the other two. The prepositions are surprisingly helpful.
I don't like to spend much time talking about the Greek, but I'll dabble in it to finish out my point. Each preposition has a variety of possible meanings, so I'll just choose the relevant meanings here:
κατὰ - (kata) "according to." We are "elect aliens" according to the Father's predetermination. Our becoming elect aliens was known in advance by the timeless Father, but more than that, His knowledge determined that it would be. We became elect aliens in perfect accordance with, in direct alignment with, the Father's knowing and determination.
ἐν - (in) "by / in." We are elect aliens by the agency of the Holy Spirit. His action resulted in us becoming these elect aliens. By His work, His power, the Father's predetermining will was completed.
εἰς - (eis) "toward / for / into." In this case, the preposition refers to a result or a goal that things move toward. We were made elect aliens for the purpose of us obeying Christ and being sprinkled clean by his sacrificial blood.
This helps us understand something about our relationship with each Person of the Trinity. The Father is the initiator in our lives, and His will determines what comes about in our lives. The work of God that is accomplished in us is done by the agency of the Holy Spirit in particular. And the goal of the Christian life is to walk in obedience to our Lord Jesus, who paid the price for our sin on the Cross.
This is not an exhaustive description of our relationships with God, of course, but seeing how each One works in our lives helps us to relate to each. We can pray to each, thank each, pay attention to each, and as we live out our lives, we can attribute particular parts of our relationship to one or the other (at least as a good working assumption).
This verse is easy to read over, but it actually is quite helpful. (It also shows that Trinitarian theology was developing very early in the minds of church leaders.)