Did Hector die

Achilles killed Hector. Hector killed Achilles best friend Patroclus so he went insane. He caught up to Hector even with Apollo's help and once he killed Hector, Achilles attached him by his achilles heel and dragged him around. This is ironic because later Paris shoots Achilles in the Achilles heel and he is vulnerable there by not being dumped into the river styx.