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)
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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)
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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)
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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)
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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)
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6 . 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)
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名校
7 . 已知四面体
是棱
的中点,设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9d86315677a86bb4dc09d06310f3f1.png)
________ (用向量
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1317c716f05a6b59afdbd0de7ba8987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc5343d0ed7b449971c7ba787a621fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9d86315677a86bb4dc09d06310f3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
您最近一年使用:0次
2024-02-27更新
|
95次组卷
|
2卷引用:山东省菏泽市2023-2024学年高二上学期期末教学质量检测数学试题
2024高二上·全国·专题练习
8 . 在直三棱柱
中,
,
,D为
的中点,在如图所示的空间直角坐标系中,
的坐标分别为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead1d5ab63a76fc1fa2b0fef17c5c009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f788fb0059b7356dc6c7811f46057e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1f47b28ba9aeaae062a569871be770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be8094e10da5b004100472adca90bdd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/9792d481-d462-48e7-a663-cb259a559751.png?resizew=136)
您最近一年使用:0次
9 . 如图所示,在平行六面体
中,
,
,
,点M是
的中点,点
是
上的点,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e983af1dfd0891d331a18e80f829c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13447f65fda380f81d32ac3d7835a887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/0d281199-39b0-4bed-a3eb-c1deb06b8e85.png?resizew=165)
您最近一年使用:0次
10 . 已知棱长为
的正四面体
中,
为
中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d692f34d059ea43d9f2508192e39238b.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d692f34d059ea43d9f2508192e39238b.png)
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