名校
1 . 在侧棱长为
的正三棱锥
中,点
为线段
上一点,且
,点M为平面
内的动点,且满足
,记直线
与直线
的所成角的余弦值的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8aca29eb6c46838852134027cf28d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01ba3f329b712e87ead41125cacd34a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
解题方法
2 . 在棱长为
的正四面体
中,点
为平面
内的动点,且满足
,则直线
与直线
的所成角的余弦值的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d124d4438fb79851ca01640f57ddc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,某正方体的顶点
在平面
内,三条棱
都在平面
的同侧,若顶点
到平面
的距离分别为
,2,3,则该正方体外接球的表面积为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f6272b0f1505f4750dbb6a49f5f6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e5f63ba3e9d264f8d3bc6829c614b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,经过边长为1的正方体的三个项点的平面截正方体得到一个正三角形,将这个截面上方部分去掉,得到一个七面体,则这个七面体内部能容纳的最大的球半径是______ .
您最近一年使用:0次
2024-04-19更新
|
1034次组卷
|
6卷引用:江苏省启东中学2023-2024学年高二年级下学期数学第二次月考
江苏省启东中学2023-2024学年高二年级下学期数学第二次月考辽宁省部分学校2024届高三第二次联考(二模)数学试题(已下线)模块4 二模重组卷 第2套 全真模拟卷(已下线)第29题 立体问题常思降维化平面,几何最值莫忘函数不等式(优质好题一题多解)(已下线)专题5 空间向量的应用问题【练】(已下线)宁夏回族自治区银川一中2024届高三下学期第四次模拟考试数学(理)试卷
解题方法
5 . 如图,在棱长为1的正方体
中,点P是对角线
上的动点(点P与点A,
不重合).给出下列结论:
平面
;
②对任意点P,都有
;
③
面积的最小值为
;
④若
是平面
与平面
的夹角,
是平面
与平面
的夹角,则对任意点P,都有
.其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339128336cb6905dc8537e58f55ad3f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15e58659e6ee4d93650e2edb6d6f7ff.png)
②对任意点P,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e49f40551cef68103af5d7d752c6878.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd5683dba7d9f29d643e9a3e3204fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a8b76e36783a69d14ec54af82c7df0.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6e96872af0f0b341835576c407e364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6e96872af0f0b341835576c407e364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00753ad7f0f49c325c387e5104f3f02.png)
您最近一年使用:0次
2024-04-10更新
|
713次组卷
|
3卷引用:上海市嘉定区2023-2024学年高二下学期期末考试数学试卷
名校
解题方法
6 . 在长方体
中,
,线段
有一动点
,过
作平行于
的平面交
与点
.当直线
与平面
所成角最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5b8a7b06dc4dc4a858cdfaa340fbc.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245c24bc367dadfa17a54f98b6552af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233015062824e26bf4b6a755c428dcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5b8a7b06dc4dc4a858cdfaa340fbc.png)
您最近一年使用:0次
解题方法
7 . 在正方体
中,
为线段
的中点,点
在线段
上,则直线
与平面
所成角的正弦值的范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/887c49fa-6f23-4808-a250-9f5fd462e828.png?resizew=172)
您最近一年使用:0次
解题方法
8 . 如图①是直角梯形
,
,
,
是边长为2的菱形,且
,以
为折痕将
折起,当点
到达
的位置时,四棱锥
的体积最大,
是线段
上的动点,则
面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cfd06965af6014208127f2880b476b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e557ac8c744f9961a6d544a75321e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1e038b4e76b3a368731d3331522b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099dd87a526391f830ac2a11e7d7ad56.png)
您最近一年使用:0次
解题方法
9 . 如图,在正方体
中,
为棱
的中点,
为棱
(含端点)上的一个动点.给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/6d6492fd-1498-49e7-aee0-3af641590d0d.png?resizew=165)
①存在符合条件的点
,使得
平面
;
②不存在符合条件的点
,使得
;
③异面直线
与
所成角的余弦值为
;
④三棱锥
的体积的取值范围是
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6293a2528570eda7fef7c784efc7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/6d6492fd-1498-49e7-aee0-3af641590d0d.png?resizew=165)
①存在符合条件的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ea211a573491409cb60f9fbe9a65cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9f260496ba23993238601a89eca5c.png)
②不存在符合条件的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7a3dc3f3a02f4400e22dec2f2fee23.png)
③异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becf2941e15d668d93ea6ed980afd0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cd8ecd9806e3a8c9b2de96110970b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31458a4ee26d560cf1f3e438f5b602.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
解题方法
10 . 已知正方体
边长为1,
,平面BED,平面
,平面
交于一点M,则点M到平面
的距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f02d5b9dcbdd711ee50a14b61219684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b698101d0a83239ce4e1d9afbb61f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda787b0b201dedd794bb8ed8989e09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4508dc6d9c91157836be679c0543cac.png)
您最近一年使用:0次