For those of us that fly without the aid of TCAS, the 'lookout and avoid' principle exists, whereby the plane on the right gives way to the right of any possible collision.
I have only had to do this once, in a glider, and found that put me in a further dangerous position.... The height of a level glider is about 5 ft to the tip of the tail. However whilst doing my turn to the right to avoid, tip of wing to tip of wing takes up about 50ft of airspace... So the other glider would have had to climb a further 25ft to avoid my wing-tip (Climb in a glider? Oh yeah!)
So the question is, do TCAS instructions rely upon each plane maintaining level flight, to avoid crossed wing problems, or is one plane sent in a climb to the right, whilst the other does an external bunt to the left.? (to keep both wings parallel)