To answer this question – eye lashes and eye brows do grow. But it depends on the length of the hair follicle growth phase.
Human hair follicles go through 3 different growth phases. Anagen – an active growth phase. During this phas the root of the hair divides rapidly and the strand grows at the rate of about 1 cm in 25 days.
Anagen phase is most important stage and end of this phase begins the next phase called catagen phase.
In this phase blood supply will cut off to the hair strand and this lasts for 2 to 3 weeks. The last phase is Telogen phase- In this phase hair gets some rest from the activity. In this phase hair begins to fall.
The reason for not long lashes and eye brows similar to scalp hair, anagen phase is responsible for this. The duration for which the hair strand stays in the anagen phase varies to different location and body knows it.
Hair follicle in the scalp usually stays in the anagen phase for 2 to 7 years and eye brow and eye lashes follicles just 30 days.
So, eye brow and lashes does not grow as long as scalp hair.