Is this permitted
There is a dispute amongst the poskim if one is allowed to smoke on a fast day particularly on the 9 Av. If there is great need one can rely on the lenient opinions although it is praiseworthy to refrain from smoking if possible. Originally I thought that electronic cigarettes might be different because the flavored vapor inhaled might be considered like drinking, but I was told that it is oil based.
O:CH 555 Mishnah Berurah 8, Shaarey Teshuvah 556:1, Eshel Avrohom (Butchach) 567, Y:D 108:5 Pischey Teshuvah 3,