My AC adapter for my psp died. I was charging the PSP with my laptop but I forgot like a week and died. My cousin has the adapter but for the PS vita, will it work?
Unfortuantely this wont work.
The PSP uses a AC adapter with a specialized tip for AC charging:
The PS vita uses a unique output port to the PSvita from a USB input:
Basically you would need a USB input that leads to a AC Tip output, which wont happen because a) they don't make these cables, b) USB output's at most 500mA which wouldn't be enough to charge the battery in most cases.
Yes, you can charge the PSP via USB with the Vita Charger/AC Adapter but not the same cable.
As RenaissanceProgrammer and Probst mentioned, the cable of the PS Vita (both OLED and LCD models) is different than the Barrel Jack that the PSP uses. To charge the PSP with the PS Vita AC Adapter (PCH-ZAC1) you will need to get a USB to Barrel Jack cable specifically for the PSP, like the one in the picture below.