Because BC⊥AB.

Namely BC⊥VAB

That's BC⊥AF

AF⊥BC

Because AF⊥VB

So AF⊥ plane VBC

(2) Using (1) to conclude the AF⊥ plane VBC.

So AF⊥VC is VC⊥AF.

Because VC⊥AE

So VC⊥ faces AEF

So FE⊥VC

(3) Because of the VBC of AF⊥ plane.

AF is in AEF, so prove it.

I didn't write it, because the conclusions I was based on were the most basic. I hope you can understand. This is the most basic)