Hi Kristian.
You're right to pick on some of my word choice.
It's been many, many years since I've taught this stuff--and I always had the advantage of being able to draw pictures.
But when I mentioned the lifting force "tilting" back with increases in angle of attack I was picturing in my head (and probably failed to convey in words) the "total" force that I would diagram with a very large arrow.
True, Lift, (the vertical component of the total force) will always oppose Gravity, and act perpendicular to the relative wind.
That vertical component of lift I would diagram with a smaller arrow, but pointing straight up against gravity.
Likewise, induced drag, the rearward component of the greater total lifting force would also be diagrammed with a smaller arrow, pointing aftward.
The large arrow, the one that represents the total of the vertical component + the rearward component, would point mostly "up" but also slightly "to the rear".
Thus I chose the word "tilt".
But you're correct, that lift (the "vector quantity" that you mentioned) will always be strictly perpendicular to the relative wind; or flight path; or even "flow direction" as you say.
I hope I've made myself clear, because we really don't disagree, we just have a different vocabulary to describe the same thing.
If we had a chalk board in front of us, this discussion would be much shorter.
