如图,矩形ABCD和梯形BEFC所在平面互相垂直,BE∥CF∠BCF=∠CEF=90°,AD= 根号3,AD与EF所成角为π/6(Ⅰ)求证:AE∥平面DCF;(Ⅱ)当二面角A-EF-C的大小为60°时,求四棱锥F-ABCD体积.蓝色为答案所做辅助
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![如图,矩形ABCD和梯形BEFC所在平面互相垂直,BE∥CF∠BCF=∠CEF=90°,AD= 根号3,AD与EF所成角为π/6(Ⅰ)求证:AE∥平面DCF;(Ⅱ)当二面角A-EF-C的大小为60°时,求四棱锥F-ABCD体积.蓝色为答案所做辅助](/uploads/image/z/8926034-50-4.jpg?t=%E5%A6%82%E5%9B%BE%2C%E7%9F%A9%E5%BD%A2ABCD%E5%92%8C%E6%A2%AF%E5%BD%A2BEFC%E6%89%80%E5%9C%A8%E5%B9%B3%E9%9D%A2%E4%BA%92%E7%9B%B8%E5%9E%82%E7%9B%B4%2CBE%E2%88%A5CF%E2%88%A0BCF%3D%E2%88%A0CEF%3D90%C2%B0%2CAD%3D+%E6%A0%B9%E5%8F%B73%2CAD%E4%B8%8EEF%E6%89%80%E6%88%90%E8%A7%92%E4%B8%BA%CF%80%2F6%EF%BC%88%E2%85%A0%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9AAE%E2%88%A5%E5%B9%B3%E9%9D%A2DCF%EF%BC%9B%EF%BC%88%E2%85%A1%EF%BC%89%E5%BD%93%E4%BA%8C%E9%9D%A2%E8%A7%92A-EF-C%E7%9A%84%E5%A4%A7%E5%B0%8F%E4%B8%BA60%C2%B0%E6%97%B6%2C%E6%B1%82%E5%9B%9B%E6%A3%B1%E9%94%A5F-ABCD%E4%BD%93%E7%A7%AF.%E8%93%9D%E8%89%B2%E4%B8%BA%E7%AD%94%E6%A1%88%E6%89%80%E5%81%9A%E8%BE%85%E5%8A%A9)
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