vain / vane / vein are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
vain: NA
vane: (noun) a fin attached to the tail of an arrow, bomb or missile in order to stabilize or guide it. (noun) the flattened weblike part of a feather consisting of a series of barbs on either side of the shaft.
vein: (noun) a blood vessel that carries blood from the capillaries toward the heart. (noun) a distinctive style or manner. (noun) any of the vascular bundles or ribs that form the branching framework of conducting and supporting tissues in a leaf or other plant organ. (noun) a layer of ore between layers of rock. (noun) one of the horny ribs that stiffen and support the wing of an insect. (verb) make a veinlike pattern.
vain: v·EY·n
vane: v·EY·n
vein: v·EY·n
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)