(1) If E is used as the ABA 1B 1 of the EG⊥ plane, then G is the midpoint of AA 1. If BG is connected, then ∠EBG is the angle formed by straight line BE and plane ABA 1B 1.

Let the side length AB of the cube ABCD-a 1 b1c1d1be1,

∴EG= 1,BE=√( 1？ + 1? +0.5? )=√2.25= 1.5,

∴sin∠ebg=eg/be= 1/ 1.5==2/3=0.666667

(2) Take point J of CD and connect BJ; On the extension line of C 1D 1 and d1k = c1d1/2, then JK∑a 1B, and JK = a1b.

∴A 1BJK is a parallelogram. The plane A 1BE is on the parallelogram A 1BJK.

∴BJ=A 1K and bj ∑ a1k.

Take the midpoint f on C 1D 1,

∫FK = FD 1+g 1K = 1/2+ 1/2 = c 1d 1 = ab 1，

∴FK=AB 1, and fk∑ab 1, ∴ a 1b 1fk are all parallelograms.

∴ b 1f//a 1k, b 1f// plane A 1BE,

∴ F exists on the edge C 1D 1 so that B 1F// plane A 1BE.

L

K

A 1 D 1

high frequency

C 1

B 1 E

Christian era

J

British commercial bank