Hand Calculations of Emitter Coupled Logic circuits
My question is how do you determine which ones are in cutoff mode and which one is on 


When you are first learning, use the method you were taught for analyzing any non-linear circuit: Guess and check. 

First guess the state of each nonlinear element. Then analyze the circuit with those assumptions. Then check that there's no logical contradiction (for example if you guessed that one of the BJT's is in saturation, then make sure you didn't calculate its \$V_{ce}\$ to be greater than 0.2 V) in the result. 

Once you've done a few problems like that you'll quickly see patterns and have a good chance to "guess" the correct states on the first try.

Like in this case, since \$V_A &gt; V_B\$, and I know that ECL logic gets its high speed from not driving BJTs into saturation, I would guess that QA is forward active and QB is cut-off.