So PA⊥BC
And BC⊥AB, AB crosses pa = a.
So BC⊥ plane PAB, and AE belongs to plane PAB:
So BC⊥AE
AE⊥PB lead cross BC = B
So AE⊥ plane PBC, and AE belongs to plane AEF.
So airplane AEF⊥ airplane PBC
(2) From (1), AE is the height of the triangular pyramid P-AEF based on PEF.
From the data in the question, we can get PB=2 root number 2, PC=2 root number 3, AE= root number 2, AF = (square root of 2 6)/3,
PE=PB/2= radical number 2, PF= radical number (PA 2-AF 2) = (2 radical number 3)/3.
The cosine theorem in triangle PBC can derive the square root of cosine angle BPC= 6/3, and then sine angle BPC = 3/3.
So the area of triangle PEF =(PE*PFsin angle BPC)/2= root number 2/3.
So the volume of the triangular pyramid P-AEF = (root number 2/3)*AE/3=2/9.