1 . 如图,在四面体
中,
是
的中点,
,设
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fc75903617d7f97f13e47091f956bc.png)
__________ .(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3a258d6685ea82beef88be6a95546e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d9ac737639ad7ce99887f9ef07685c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20a9410ceb649e303910f8efe5f7531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbadd77fde781d924b14e6dc57505ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fc75903617d7f97f13e47091f956bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
您最近一年使用:0次
2 . 如图,在四棱锥
中,底面
为菱形,
,
,
为棱
的中点,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d476da94dcade5f83541f3fca22a1039.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970bd8c6012979f91c4b370fad352d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20f88c036d89f947473c4e831d565da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d476da94dcade5f83541f3fca22a1039.png)
您最近一年使用:0次
名校
解题方法
3 . 《九章算术》中的“商功”篇主要讲述了以立体几何为主的各种形体体积的计算,其中堑堵是指底面为直角三角形的直棱柱.如图,在堑堵
中,
分别是
,
的中点,
是
的中点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d81947c03e5677e0d8828fe7fcd7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
您最近一年使用:0次
名校
4 . 在四面体OABC中,
是棱OA上靠近
的三等分点,
分别是
的中点,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33a7fe8acce3fc214d44459e92ffa97.png)
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518407c06c4c966f670ea9d2414984a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa87ac2b7d6a58f5aaee923d83f799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33a7fe8acce3fc214d44459e92ffa97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71af5e80069433636f4ef0227a508dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8d49bf33e578b25811e22e26dbf584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
您最近一年使用:0次
5 . 在三棱锥
中,
和
都是等边三角形,
,D为AB中点,则
的值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa9fa88d321bc55ca505771d77dc405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1605925e08c31d30c193c4321aacba26.png)
您最近一年使用:0次
解题方法
6 . 在矩形
中,
,
,沿对角线
将矩形折成一个大小为
的二面角
,当点B与点D之间的距离为3时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4961a7dd688b8a12db7d1d3480c6b87f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4746df85049d1651d3f6c30212a7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4961a7dd688b8a12db7d1d3480c6b87f.png)
您最近一年使用:0次
23-24高一下·全国·随堂练习
解题方法
7 . 如图,向量
,
,
,则向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec33b8270e7493da5408ddc3e9848e2.png)
_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac55753625e93fc8fb327f9262d41b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec33b8270e7493da5408ddc3e9848e2.png)
您最近一年使用:0次
8 . 如图,在棱长为
的正方体
中,
在棱
上,且
,以
为底面作一个三棱柱
,使点
分别在平面
上,则这个三棱柱的侧棱长为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae29000bb323cdde854b9b2990702106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74bd812e68ff60c201ab36f33305f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6dec2c74186d6a781e0c38ad794a225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f6c3f861c5d2eaeb82cee88e70fb69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6125a3317868d056dc1355c2f6f260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d12391c3c228ba27ecb2c23afc39008.png)
您最近一年使用:0次
9 . 如图,设
为
所在平面外任意一点,
为
的中点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc840e197de2dabff676ee1b8968fada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8c9a4f4f4a64ba852a1346c10113ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/5c8fb242-2ca6-45f2-af26-ac1937778622.png?resizew=142)
您最近一年使用:0次
10 . 如图,在长方体
中,已知
,
,
,若对角线
上存在一点
,使得
,则
的最大值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e0d2c3608c31abe8a71da91dcfd70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59f7400fc9ba75e12991a49adcf1f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641420d1ceecfa4531725fefeba60009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d62b6e7d719835c9fca341eb1398977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3438f9487fc17c3b67a4706733378568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd3dbc21137cc3dd200ca4bfe8a01e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2275c7753ff84e491cb18ce86cde3713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74eed0cd9cfbff4e684215492846610e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/59df956c-8433-4a78-b613-5598051014ce.png?resizew=151)
您最近一年使用:0次