要证A1F垂直平面BED,只要证A1F垂直平面BED内的两条相交直线即可.连A1F,FE,A1E,现在来证明A1F垂直BD,A1F垂直EF.设正方体楞长为1.则AC=根号2,AF=根号2/2,因为三角形AA1F是直角三角形,由勾股定理求得A1F=根号6/2,而A1B=...