Vent size and building stability question

[Pangea]

Are you talking about cutting just through the header/rim joist? 7" is a big hole on a 10" joist.
If its through a reg floor joist spanning an empty space there are very specific sizes your board can sustain.

 

[Ref1]

Yes, it's a header board. The one that all joists connect in perpendicular fashion. Is there any way to enforce it? I already ordered 12x6 rectangular duct. I was about to cut a hole this size. And I actually need 4 of them on the same wall. 2 holes for flower room air (in/out) and 2 for window AC in/out.