(1) It is proved that the side aa1c1of the ∵ regular quadrangular prism ABCD-a1is a rectangle with side length AB=2a and BC=a, and e is C.

∴EC=ED=2a,CD=2a

∴EC⊥ED, ... (2 points)

∵BC⊥ plane CC 1D 1D, DE? Plane CC 1D 1D,

∴BC⊥DE, ... (4 points)

∫BC∩EC = C

∴DE⊥ Aircraft EBC, …(7 points)

(2) solution: ∫AD∨BC,

∴∠EBC is the included angle (or remaining angle) of straight lines on different planes, …(9 points)

Take BC⊥ plane CC 1D 1D, EC? BC⊥EC Plane CC 1D 1D, …( 1 1)

That is, △EBC is a right triangle,

In the right angle △EBC, EC=2a, BC=a,

∴tan∠EBC=ECBC=2

∴∠ EBC = Arctan2...( 14 points)