Depends on the type of smoke detector, I tried exhaling vapor once into mine and it went off. The older models used to use a radioactive compound called americium-241, which emits a constant stream of alpha particles to detector plates around it, if the stream is broken due to refraction of the alpha particles due to vapor, smoke, highly concentrated steam, etc... then the alarm would go off. This is why the old, "fan it with a towel" method works even if the blocking particles are still present, since the smoke detector would have a constant air gradient moving the refracting particles away from the detecting plates.
As mentioned before, vape towards the floor or in the opposite direction to the detector and you'll be fine as the particles will dissociate into the air (decreasing concentration/volume of air present) before they reach the detector.
That being said, if you are in a very small space and you chain vape, a sensitive beam detector COULD go off, but the chances are unlikely, especially if you blow air from your lungs into the vapor cloud after exhaling as that will speed up the dissociation process.