I didn’t really understand how cross product and chirality relate? You might want the x and z coordinates to have a correct y coordinate for aesthetic reasons but what does that have to do with the perpendicular line direction to any random plane in 3d space? How does a random plane have coordinate system correct perpendicular line direction? (I guess since any random vector begins at the origin all the random planes intersect the origin) Is there any use to the getting the cross product with the proper coordinate system direction other than convention?

Normal vector direction in games is usually determined by inside vs outside of an object rather than the coordinate system right?

Also what did you mean when you said flipping the vectors? Did you mean multiplying them by -1?

Secondly how would you know which vector to multiply first to get a vector direction according to the proper coordinate system?