For this kind of problem, the department must choose a suitable origin. If the problem does not give a suitable origin, we can find a suitable point through the given conditions. This question:

∵PA⊥ ABCD at the bottom, ABCD is a diamond, ∴AC⊥BD, located in O.

Establish a spatial rectangular coordinate system O-xyz with O as the origin, AC as the X axis, BD as the Y axis and AP as the positive direction of the Z axis.

∫AC = 2√2, PA=2, E is a point on the PC, PE=2CE.

Then point coordinates:

O(0，0，0)，A(-√2，0，0)，C(√2，0，0)，P(-√2，0，2)，E(√2/3，0，2/3)，B(0，-y，0)，D(0，y，0)

Vector PC = (2 √ 2,0, -2), vector EB = (-2/3, -y, -2/3), vector ED = (-2/3, y, -2/3).

Vector PC* vector EB =-4/3+0+4/3=0.

Vector PC* vector ED =-4/3+0+4/3=0.

∴PC⊥ surface

(2)∵ When the dihedral angle A-PB-C is 90, ∴ the bottom ABCD becomes a square (also a diamond), and the system can be established as the answer.