名校
1 . 如图,在三棱锥
中,平面
平面
为棱
上靠近点
的三等分点,且
为
的角平分线,则二面角
的平面角的正切值的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74684c76385a0240f1e9b7f22202ef12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/16513c35-d137-41b3-ad20-4b4258f1d346.png?resizew=154)
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3卷引用:贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题
名校
解题方法
2 . 现准备给一半径为
的实心球体玩具制作一个圆台型带盖的纸质包装盒,要使制成的包装盒能装下该球体玩具,且该包装盒的下底面是半径为
的圆,则制成的包装盒的容积最小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/01cbcbe2-203d-403e-bf58-0aedae50cda3.png?resizew=162)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-04更新
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3卷引用:贵州省黔东南苗族侗族自治州2023-2024学年高三上学期九校联考(开学考)数学试题
3 . 如图,在四棱锥
中,四边形
是菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/f3a6b22b-d1a0-40f1-9c9c-6ffb655cd8cd.png?resizew=170)
(1)证明:平面
平面
.
(2)求二面角
的余弦值.
![](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/917059c4d68de6935b5b010edd3b2efb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/f3a6b22b-d1a0-40f1-9c9c-6ffb655cd8cd.png?resizew=170)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b31c44f920e6e09b02f03ec82ef843.png)
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2024-03-03更新
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4 . 已知
、
,且
与
夹角为钝角,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0886c7951d69985cad4948d3291a5c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8231fd1454986d4d49fee4006a28edd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题
贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题江苏省南京市第九中学2023-2024学年高二上学期期末数学试卷(已下线)模块一 专题5 《空间向量运算》(苏教版)(已下线)高二 模块3 专题1 第2套 小题入门夯实练(苏教版)
名校
解题方法
5 . 如图所示,在圆锥内放入两个球
,它们都与圆锥相切(即与圆锥的每条母线相切,切点圆分别为
.这两个球都与平面
相切,切点分别为
,丹德林(G.Dandelin)利用这个模型证明了平面
与圆锥侧面的交线为椭圆,
为此椭圆的两个焦点,这两个球也称为G.Dandelin双球.若圆锥的母线与它的轴的夹角为
,
的半径分别为2,5,点
为
上的一个定点,点
为椭圆上的一个动点,则从点
沿圆锥表面到达
的路线长与线段
的长之和的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096cd7bd8a5a2219fd7dd166bbb8460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9980316b84e2702c4c40eaca97afe3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9980316b84e2702c4c40eaca97afe3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ba050bb69ab55bdcb96f935f5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/d28f4c2a-003e-4091-adb4-62f09a977bf2.png?resizew=128)
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2卷引用:贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题
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6 . 在空间直角坐标系中,
表示经过点
,且方向向量为
的直线的方程,则点
到直线
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452af21e95f71dc626c04fafafd8ca49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9f353152c7f589c0caf5f964f803ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75e40962be6a0766e58ab3c2ac42816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10cf8d3369477b047830fca8e572ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda6b424560ae0936d0dc9dd399915fd.png)
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解题方法
7 . 如图,在棱长为1的正方体
中,点
在侧面
内运动(包括边界),
为棱
中点,则下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/35172246-ad30-4a32-96f3-aec18508fac1.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/35172246-ad30-4a32-96f3-aec18508fac1.png?resizew=165)
A.存在点![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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6卷引用:贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题
贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题重庆市南开中学校2024届高三上学期第五次质量检测数学试题重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题江苏省扬州市扬州中学2024届高三上学期1月阶段性检测数学试题辽宁省沈阳市、大连市2023-2024学年高二上学期教学联盟大联考数学试题(已下线)第三章 空间轨迹问题 专题六 立体几何轨迹中的范围、最值问题 微点1 立体几何轨迹中的范围、最值问题【培优版】
名校
8 . 如图,在四面体
中,
是棱
上靠近
的三等分点,
分别是
的中点,设
,
,
,用
,
,
表示
,则 ( )
![](https://img.xkw.com/dksih/QBM/2024/1/24/3418166278266880/3418286791098368/STEM/fb4583c6bf7846dbab774850b17f86dd.png?resizew=183)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.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/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd14dfc0024459f9d8e594c95c5106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07dcf0b16163e0e0e0c0f248466ee7e.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/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://img.xkw.com/dksih/QBM/2024/1/24/3418166278266880/3418286791098368/STEM/fb4583c6bf7846dbab774850b17f86dd.png?resizew=183)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:贵州省铜仁第一中学2023-2024学年高二下学期2月开学适应性模拟检测数学试题
名校
解题方法
9 . 如图,在正方体
中,
,
分别为
,
的中点,则异面直线
与
所成角的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
10 . 已知梯形
,
,
,
,
,
是线段
的中点.将
沿着
所在的直线翻折成四面体
,翻折的过程中下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() ![]() |
B.当直线![]() ![]() ![]() ![]() |
C.四面体![]() ![]() |
D.四面体![]() ![]() |
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