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(文)如图,已知长方体ABCD-A1B1C1D1中,AB=BC=1,BB1=2,连结BC1,过点B1作BC1的垂线交CC1于E.
(1)求证:AC1⊥平面EB1D1;
(2)求三棱锥C1-B1D1E的体积.