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如图所示,在四棱柱eqId588284d93dc5489295f8f224f8e30d13中,侧棱eqIdf2d7ae1e12d741159b2987d4e1d63952底面eqId5ce7a06ae7a34393b92b5277978ac014eqIdce6f97e7da6d4498b480e6ab85254753eqIdfc9e3955752c4ef1a6d934498d728ff6eqId72fe3587d8244374a2b6a0904fb8d261eqIdd0c1d3d84e78446d84e4391e8a3c5e09eqIdee238f8b821545159c8f269a5acc96bfeqId8756af76be5b4ee3a6fb9b2dc685d798
figure
(1)求证:eqId2ad03ecc39f3413f85f3b0684c3bb0ab平面eqIde37223a82dd14db39016756bd377dd6d
(2)求直线eqIdea82c30b37894b1bb742dee61200db07与平面eqId5b01d44ca6924509ab97873523b3a8ad所成角的正弦值.
更新:2020/07/14难度:0.65题型:解答题组卷:114
在直三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43中,若eqIddd8f7239d0584083b60302e6e39c1333eqIdbfedf6f0d400489d8d7d323633bf2d14,则异面直线eqIda53f4cdd3230496d942add97720f07d9eqId0abb42be2cff41118ff3f94f13428c16所成角的余弦值为(   )
A.eqIdcf32b3b919f04cc18988c622e750e9f1B.eqIdd90d42b6b616485585b2c5a5bd194eb6C.eqIda86879ae304449a4a6e6461c485a1f13D.eqId650bf73d6b904c6a9ee39b0dc18fea28
更新:2020/07/14难度:0.85题型:单选题组卷:94
如图,四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,平面eqId3084aa1e379e4f168e9c2332df2ca9df底面eqId5ce7a06ae7a34393b92b5277978ac014eqId51f3ec023aab4a4ca875aaacec8ee06b是等边三角形,底面eqId5ce7a06ae7a34393b92b5277978ac014是菱形,且eqId0e67152dca434884938a186e656be4c5eqId2381423d4cd146cab95f55527681a766为棱eqIdd293923b221045898dcc5442f88aa67a的中点,eqId517584fed25c413ba8b7bb33ffa2d5c6为菱形eqId5ce7a06ae7a34393b92b5277978ac014的中心,下列结论正确的有(   )
figure
A.直线eqIde9b50933e347462ea824ccc9bf51fc93与平面eqIdd235c463973544ba97988f64fd7a6f81平行B.直线eqIde9b50933e347462ea824ccc9bf51fc93与直线eqIdbf4db7d066034b139ff80a09ab139d45垂直
C.线段eqIdc7fb590d53e8494da0bf95591471c64b与线段eqId8bf9f946e82248fea882e001e101c571长度相等D.eqIde9b50933e347462ea824ccc9bf51fc93eqIdc7fb590d53e8494da0bf95591471c64b所成角的余弦值为eqIdfc2bc31fcbdf4db399efd669abc4d214
更新:2020/07/14难度:0.65题型:多选题组卷:227
三棱锥eqId12175c05cfe240a0b8270ee03df1962f中,eqId50f1173522d8464db0a444ce1878dbef,且平面eqId21d75cb53dbf45f6bbe6a9c4546d7179平面eqId89fbdcb029be4482b52165366491c70f,则eqId2ab613dbc09c426e8a0a9316b7e6ff0a__________;若球eqId2efda802d5534f6d92d9f8af7aaec28b与该三棱锥除eqIde9b50933e347462ea824ccc9bf51fc93以外的5条棱均相切,则球eqId2efda802d5534f6d92d9f8af7aaec28b的半径为__________.
更新:2020/07/14难度:0.65题型:双空题组卷:138
如图,正方形eqIdb59c5c70f4c74abb9a5b39e8e9b43f06的边长为2,eqId935f449333634ac0b951c0ff438be81c分别为线段eqIdbc505cd6ce174e46bdf97b329668236e的中点,在五棱锥eqIdb4d41cf91a074ebdb150f8e2d55703f7中,eqId63db14a5b4334f3ea583c8fb12b0d175为棱eqId9608739a1d8547df8df8461d80f9f5f2的中点,平面eqIdedf40810b0c249f7a28084bb4ec2edc4与棱eqIdb4f0e9d544034fdb9cdcea36cb8c2370分别交于点eqId2465fec2c14444b488c9162b035cc230
figure
(1)求证:eqId75bcf0a5f4044c6b8eccc7edad658458
(2)若eqIde78cce043a6c43329b55788351ff3484底面eqIdcfdc118cc3484494b8ee9d75ea8b8fc2,且eqId04d8e610d1944d9d9e031c0071646dae,求直线eqId0627be51821d4be7b3e024a354815d64与平面eqIdedf40810b0c249f7a28084bb4ec2edc4所成角的大小.
更新:2020/07/13难度:0.65题型:解答题组卷:1016
已知四边形eqId5ce7a06ae7a34393b92b5277978ac014为矩形,eqIdfd6adaef2b94437db6c1fa81276d9f8bEeqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点,将eqIdac60916bbf2249d5b0d373c8d6bd2d84沿eqId66d409c343f04cfda647f9bfc7da6b2a折起,连接eqId30ace6b4ce264294a0534221c1b01e26eqId710b690db05c4a9ca514d234b961f314,得到四棱锥eqIde698b2b882ef438c97b82e5bf1a7250fMeqId710b690db05c4a9ca514d234b961f314的中点,eqId3dd88fd134c1472886302db0246dfc44与平面eqId5ce7a06ae7a34393b92b5277978ac014所成角为eqIdc13953f2514e4c8f9c8aaaf5241c33ac,在翻折过程中,下列四个命题正确的序号是________.
eqIdd69e71204ce5415cb5d1d5bf85914544平面eqIde932a97fc208440ea8df9ac8c7f6baf9
②三棱锥eqId30bc9801a9d24f9187156e41bacd3340的体积最大值为eqIdd1ebfa5c81a04d18900d19595d070677
③点M的轨迹是圆的一部分,且eqIdc7a68dde133b46739f97bb287b6b6de8
④一定存在某个位置,使eqId86761d9342cc4ddd87c727bbc3d68c20说明: figure
更新:2020/07/13难度:0.4题型:填空题组卷:0
如图,在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqIdc3bc315778fd47ef9822f0554c98bd79分别是棱eqId0627be51821d4be7b3e024a354815d64eqId3549028b0a264a919e61d7f350198187的中点,则eqId1a0830891ff846de8422ea80714ecab4与平面eqId6b74a67a320746f3818d49426f4b17a6的位置关系是(   )
说明: figure
A.eqIda5e4dd5d4b81428cbff4de50c7bf234c平面eqId6b74a67a320746f3818d49426f4b17a6B.eqId1a0830891ff846de8422ea80714ecab4与平面eqId6b74a67a320746f3818d49426f4b17a6相交
C.eqId1a0830891ff846de8422ea80714ecab4在平面eqId6b74a67a320746f3818d49426f4b17a6D.eqId1a0830891ff846de8422ea80714ecab4与平面eqId6b74a67a320746f3818d49426f4b17a6的位置关系无法判断
更新:2020/07/13难度:0.65题型:单选题组卷:0
下列说法错误的是(   )
A.平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac与平面eqId4eb56f42ca674f2f9c9101b548763159相交,它们只有有限个公共点
B.经过一条直线和这条直线外的一点,有且只有一个平面
C.经过两条相交直线,有且只有一个平面
D.如果两个平面有三个不共线的公共点,那么这两个平面重合
更新:2020/07/13难度:0.85题型:单选题组卷:267