The VISTA near-infrared YJK _ { \mathrm { s } } survey of the Magellanic System ( VMC ) is collecting deep K _ { \mathrm { s } } -band time–series photometry of pulsating stars hosted by the two Magellanic Clouds and their connecting Bridge .
Here we present Y, J, K _ { \mathrm { s } } light curves for a sample of 717 Small Magellanic Cloud ( SMC ) Classical Cepheids ( CCs ) .
These data , complemented with our previous results and V magnitude from literature , allowed us to construct a variety of period–luminosity and period–Wesenheit relationships , valid for Fundamental , First and Second Overtone pulsators .
These relations provide accurate individual distances to CCs in the SMC over an area of more than 40 deg ^ { 2 } .
Adopting literature relations , we estimated ages and metallicities for the majority of the investigated pulsators , finding that : i ) the age distribution is bimodal , with two peaks at 120 \pm 10 and 220 \pm 10 Myr ; ii ) the more metal-rich CCs appear to be located closer to the centre of the galaxy .
Our results show that the three–dimensional distribution of the CCs in the SMC , is not planar but heavily elongated for more than 25-30 kpc approximately in the east/north-east towards south-west direction .
The young and old CCs in the SMC show a different geometric distribution .
Our data support the current theoretical scenario predicting a close encounter or a direct collision between the Clouds some 200 Myr ago and confirm the presence of a Counter-Bridge predicted by some models .
The high precision three–dimensional distribution of young stars presented in this paper provides a new testbed for future models exploring the formation and evolution of the Magellanic System .