∵该图形为长方体,AA1=AD
∴四边形AA1D1D是正方形
∴对角线AD1垂直于A1D
∵EA垂直于面AA1D1D
∴EA垂直于A1D
∵A1D垂直于AD1,A1D垂直于AE
∴A1D垂直于AA1E
∴A1D垂直于D1E