Question

三棱锥P-ABC,PB垂直于底面ABC,角BCA=90°,PB=BC=CA=2,E为PC中点,点F在PA上,且2PF=F

Answer 1

∵PA⊥面ABC,∴BE⊥PA.

∵△ABC是正三角形,∴AB＝BC,又AE＝CE,∴BE⊥AC.

由BE⊥PA、BE⊥AC、PA∩AC＝A,得：BE⊥面PAC,∴面PBE⊥面PAC.