As shown in the figure, in the triangular prism abc-a1b1c1, the side edge Aa1 ⊥ bottom surface ABC, ab ⊥ BC, D is the midpoint of AC, A1A = AB = 2. (1) prove: Ab1 ∥ plane BC1D; (2) through point B, make be ⊥ AC at point E, prove: straight line be ⊥ plane aa1c1c1c (3) if the volume of pyramid b-aa1c1d is 3, calculate the length of BC

As shown in the figure, in the triangular prism abc-a1b1c1, the side edge Aa1 ⊥ bottom surface ABC, ab ⊥ BC, D is the midpoint of AC, A1A = AB = 2. (1) prove: Ab1 ∥ plane BC1D; (2) through point B, make be ⊥ AC at point E, prove: straight line be ⊥ plane aa1c1c1c (3) if the volume of pyramid b-aa1c1d is 3, calculate the length of BC

(1) Let B1C ∩ BC1 = O, connect OD ∩ bcc1 & nbsp; B1 as a parallelogram, O as the midpoint of B1 & nbsp; C, D as the midpoint of AC, OD as the median line of △ ab1c, BC1D & nbsp; OD ⊂ bc1dab1 ⊊ BC1D; (2) ∨ A1A ⊥ plane a