(文科做)(本题满分14分)如图,在长方体 ABCD—A1B1C1D1中,AD=AA1=1,AB=2,点E在棱AB上移动. (1)证明:D1E⊥A1D; (2)当E为AB的中点时,求点E到面ACD1的距离; (3)AE等于何值时,二面角D1—EC-D的大小为. (理科做)(本题满分14分) 如图,在直三棱柱ABC – A1B1C1中,∠ACB = 90°,CB = 1, CA =,AA1 =,M为侧棱CC1上一点,AM⊥BA1. (Ⅰ)求证:AM⊥平面A1BC; (Ⅱ)求二面角B – AM – C的大小; (Ⅲ)求点C到平面ABM的距离. |