一Oh，it's really old．I       it for lo years．

   When Bill is very young, he loves picture. His mother often draws some for him on old pieces of paper. She is very bad at drawing, but bill likes her pictures and always wants more. Then, when he is a little older, Bill’s mother gives him some pencils and a drawing book, and he begins drawing pictures, too. But they are never good .When Bill is five years old, his mother gives him a small blackboard and some pieces of a baby on the blackboard, he draws lines(线条) and rubs(擦) them out too for ten minutes , but when he looks at his picture , he is not happy. “Well”, he says at last(最后) to his mother, “I’ll put a tail(尾巴) on it and make it a monkey.”

（Ⅰ）若点G是棱AB的中点，求证：EG∥平面BDF；

（Ⅱ）求直线AE与平面BDF所成角的正弦值；

（Ⅲ）在线段FC上是否存在点H，使平面BDF⊥平面HAD？若存在，求 $\frac{FH}{HC}$ 的值；若不存在，说明理由．