dwv
The lack of a trap in your drawing has nothing to do with it. The configuration of the drain line would turn whatever trap you use into an "S" trap and they are illegal. The vent can come off the horizontal line anywhere between the trap and the downturning 45. The only way to make what you have "legal" would be to connect the sink to the 3" riser, then run the sink vent to the attic and connect back to the main line at the point where you increase to 3". You would also have to extend the tub trap into the attic and tie it into the main line. Either both vents would have to connect at the same point, or the lower one would have to be where you increase to 3". In addition ONE of the two drains and vents, sink or tub, would have to be 2", the other could be 1 1/2".