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如图，菱形ABCD的边长为6，∠BAD=60°，AC∩BD=O．将菱形ABCD沿对角线AC折起，得到三棱锥B-ACD，点M是棱BC的中点， DM=3 2 ． （Ⅰ）求证：OM ∥ 平面ABD； （Ⅱ）求证：平面ABC⊥平面MDO； （Ⅲ）求三棱锥M-ABD的体积．
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