名校
解题方法
1 . 若
均为单位向量,下列结论中正确的是_______ (填写你认为所有正确结论的序号)
(1)若
且
,且
,则
的取值范围为
;
(2)若
且
,且
,则
的取值范围为
;
(3)若
且
对任意实数
恒成立,则
的最小值为
;
(4)若
且
对任意实数
恒成立,则
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae19a80b97d4dfd1be47844c02980d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3797ac9ea94855ed77cb9be5b4671874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d6f122739bfe3e5182375b585870a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c73388e5a836011f59e523130b0784.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae19a80b97d4dfd1be47844c02980d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29119d4f3ee3426a24700ff7b4ba3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d6f122739bfe3e5182375b585870a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93188fdb80dbd006ff8e940f048896a7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960fffaf9d3cee05667705c83419380e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8891c4e0d2d98d3070164b4a48f5d692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c279eca88d292dd0573b49efae2e07f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960fffaf9d3cee05667705c83419380e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8891c4e0d2d98d3070164b4a48f5d692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aafdbb391ae0050cef40c8d590cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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名校
解题方法
2 . 《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
3 . 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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4 . 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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解题方法
5 . 在四面体
中,
,
,
,设四面体
与四面体
的体积分别为
、
,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8c3adfb5c3cb6dd9ba688856e2dd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90592be71b12efb676770f65d68596f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1bb96d6663c8cdbf43ba53e1505e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f107bd06ad6af2ff8d5aaa9ace12d9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae00abada46919dffcfb342971dcdabd.png)
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名校
解题方法
6 . 正三棱锥
中,底面边长
,侧棱
,向量
,
满足
,
,则
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da3fdf44b48a0d66b87441fc699cab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b396937ce186ccb792210cb7b852f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ca854e782895e8f5f08a65dce610c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e6f98f23fea7db0f74897928024ca0.png)
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2024-04-01更新
|
1143次组卷
|
6卷引用:上海市浦东新区2024届高三下学期期中教学质量检测数学试卷
上海市浦东新区2024届高三下学期期中教学质量检测数学试卷(已下线)压轴小题5 空间向量中的最值问题江苏省姜堰中学2024届高三下学期阶段性测试(2.5模)数学试题(已下线)数学(上海卷01)(已下线)压轴题06向量、复数压轴题16题型汇总-1上海市吴淞中学2023-2024学年高二下学期第二次调研(5月)数学试卷
解题方法
7 . 如图,在平行四边形中,
,
,且EF交AC于点G,现沿折痕AC将
折起,直至满足条件
,此时EF的长度为
您最近一年使用:0次
名校
8 . 某圆锥的轴截面是边长为4的正三角形,
是底面圆的一条直径,
是侧面上一动点,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
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9 . 在三棱柱
中,
,
,且
平面
,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d74b1d0480790400a9223e4437afdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7dc14ef100b26679193fb93f3a8b5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214481e6b23307a37940f6dd0313d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4e7552a39c412d882766dbcd7eeb69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 如图,在四面体
中,
分别是
上的点,且
是
和
的交点,以
为基底表示
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a337a934b801730321f67b0e5a0b144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85a08b7404da7ee0fa373540966176b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f1f880e5ffbff036953acaca90c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1408c55c40465b26758562f59d99ae41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/fb89f17c-87a6-403f-bc75-f41656266583.png?resizew=154)
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