充值 服务号
首页>高中数学综合库>空间向量与立体几何>点、直线、平面之间的位置关系>直线、平面垂直的判定与性质>面面垂直的判定>证明面面垂直
题型:解答题 难度:0.65 引用次数:30 更新时间:2020/3/26 11:11:53 题号:9868530
四棱锥eqIddd5f333edd7c4a01b271754239943f8d中,eqIdade7975ad42c46d4b9aada13bc22c654平面eqId5ce7a06ae7a34393b92b5277978ac014,底面四边形eqId5ce7a06ae7a34393b92b5277978ac014为直角梯形,eqId397c03e525444a989afc6269369b5cdbeqId1acddecbe2a24d149cbad7e37b42bc75eqId631983261edb4c49a81fb7a7fc943d09eqId790707287e604e1a97e1484c1457c054.
figure
(Ⅰ)求证:平面eqId1696ce98d8ce40588bd2be63a1ef4872平面eqId911194e8bdd14e3a943a486588dc8285
(Ⅱ)求二面角eqIdf0265b51bb6542928884244dfee4aa1a的余弦值;
(Ⅲ)eqId2381423d4cd146cab95f55527681a766eqId17cf387aa11242af969dcfd73db2a4d5中点,在四边形eqId5ce7a06ae7a34393b92b5277978ac014所在的平面内是否存在一点eqId517584fed25c413ba8b7bb33ffa2d5c6,使得eqIdefbe4303bc964cb1bc3a76d308ba961d平面eqId11a1b1d16a2e412784a39dba2b832898,若存在,求三角形eqIddb22c9f59e504a6eb95ad922507412ed的面积;若不存在,请说明理由.

类题推荐

【推荐1】如图,三棱柱ABCA1B1C1各条棱长均为4,且AA1⊥平面ABCDAA1的中点,MN分别在线段BB1和线段CC1上,且B1M=3BMCN=3C1N
figure
(1)证明:平面DMN⊥平面BB1C1C
(2)求三棱锥B1DMN的体积.
更新:2020/02/12难度:0.65题型:解答题组卷:92
【推荐2】如图,四棱锥eqIdac097205e9cb41279269aadcac3fb6f1的底面eqId5ce7a06ae7a34393b92b5277978ac014是矩形,eqId4029455ff5bf4551be55dc2827040c0c,点eqId93cbffaa5ae045d6ac45d1e979991c3aeqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,eqIdcf2da96900c948a1b3ce7cbfd420c080eqId1b51efe7c2fa42748ac5a6be262e2fa4交于点eqIdaad7b72a25924d078d2360cdc99f1090.
figure
(Ⅰ)求异面直线eqIda4133d812272499891a1f8813d5747f8eqIdbf4db7d066034b139ff80a09ab139d45所成角的余弦值;
(Ⅱ)求证:eqId0732f97a73314df8af1fcbeca4aa9877
(Ⅲ)求直线eqId6f782d71f5a7422aa78bd8204949ce26与平面eqIdef6a7c356a884ffc866777aa14a0f89b所成角的正弦值.
更新:2020/05/13难度:0.65题型:解答题组卷:757
【推荐3】如图,在三棱锥eqId3a31af2cac704f7882626fb78089ea14中,eqId5bb805ad40d84aacb1ffe30d898ea46beqId157b14c424eb497a9ec32b6a14381cd0eqIda18c9737a97a474cb66b31021c50ee5aeqId19f97bded86b49138f9cccc65ed75269分别为eqId785ef24bba004f99b5496cc095f4a184的中点,eqIdd5b10b2a13f148b78e0d5a1b820538fd为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3上一点.
(1)证明:eqIdbe31e03f1e324041a582ba313f26a06f平面eqIde499a0d7181a4bf4bfcd70c68255bab7.
(2)证明:平面eqIda317d6e48b6e42c4a05571221212a6f0平面eqId89fbdcb029be4482b52165366491c70f.
(3)若平面eqIde7b4f0c0980e4573a93a266e6dbc7f56平面eqIde499a0d7181a4bf4bfcd70c68255bab7,证明:eqIdd5b10b2a13f148b78e0d5a1b820538fd为线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点.figure
更新:2017/11/19难度:0.65题型:解答题组卷:381