Solution: ∵AC⊥ plane BB 1D 1D, and BE? Plane BB 1D 1D

∴ communication ⊥ yes Therefore, ① is correct.

∵b 1d 1∑ plane ABCD, e and f move on the straight line D 1B 1

∴EF∥ plane ABCD .. Therefore, ② is correct.

③ Because the distance from point B to the straight line B 1D 1 remains unchanged, the area of △BEF remains unchanged.

The distance from point A to plane BEF is 0, so VA-BEF is a constant value. ③ Correct.

When point E is at D 1 and f is the midpoint of D 1B 1, the angle formed by AE and BF is ∠ OD1a.

When E is at the center of the upper bottom surface, F is at the position of B 1, and the angle formed by the straight lines of AE and BF on different planes is ∠OEA.

Obviously, the two angles are not equal.