Ac and BD intersect at f and connect PF, knowing that PF is perpendicular to the bottom ABCD.

First, we get the following results: the height of the prism PF=h= (root number 2)/2, the side length of the bottom a= root number 3, the diagonal AC= the square root of 6, and the side PC= root number 2.

Connecting EF is based on the midline theorem, EF//AP. TherEFore, the angle BEtween ef and BE is the angle between PA and be.

Since BF is perpendicular to AC, BF is perpendicular to PF and PF is perpendicular to PAC, PF is perpendicular to EF.

That is, the triangle EFP is a right triangle, BF = (square root of 6) /2, EF= (root number 2)/2 (right triangle, the median line on the hypotenuse is equal to half of the hypotenuse).

Therefore: tan (angle FEB)=BF/EF= root number 3. That is, the known angle FEB=60 degrees.

That is, the angle BEtween PA and be is 60 degrees.