1 . 如图,已知正方体
的棱长为2,点
为
的中点,点
为正方形
上的动点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/53127c91-1028-4c04-a6c4-540f58701ca2.png?resizew=207)
![](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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/53127c91-1028-4c04-a6c4-540f58701ca2.png?resizew=207)
A.满足![]() ![]() ![]() ![]() |
B.满足![]() ![]() ![]() |
C.存在唯一的点![]() ![]() |
D.存在点![]() ![]() |
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9卷引用:广东省梅州市2021-2022学年高二下学期期末数学试题
广东省梅州市2021-2022学年高二下学期期末数学试题福建省福州第一中学2022-2023学年高二上学期期末数学试题(已下线)1.3.2 空间向量运算的坐标表示(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)第03讲 空间向量及其运算的坐标表示(7大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)河南省濮阳市2023-2024学年高二上学期9月大联考数学试题陕西省西安市长安区2023-2024学年高二上学期10月月考数学试题福建省福州教育学院附属中学2023-2024学年高二上学期期末考试数学试题安徽省阜阳市阜阳一中2023-2024学年高二下学期开学检测数学试题贵州省都匀兴华中学2023-2024学年高二上学期阶段测试(一)数学试题
名校
2 . 如图,矩形
中,
,
为边
的中点,将
沿直线
翻折至
的位置.若
为线段
的中点,在
翻折过程中(
平面
),给出以下结论:
①三棱锥
体积最大值为
;
②直线
平面
;
③直线
与
所成角为定值;
④存在
,使
.
则其中正确结论的序号为_________ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8588e18e27bfebf7c81c7e3c7efb1149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb79f948d408ab4fb6708bde172c5e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b9f96b8ecc3cb000bb2f030809f225.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c70966a318ef8ecf874257f5c5e5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
④存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2181c78134c310f746eab44b9124e63b.png)
则其中正确结论的序号为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/2/db8c3c80-3639-479e-8ae4-e7aeaef6394b.png?resizew=239)
您最近一年使用:0次
2022-07-01更新
|
1377次组卷
|
5卷引用:山西省太原市2021-2022学年高一下学期期末数学试题
名校
3 . 在棱长为1的正方体
中,点M是
的中点,点P,Q,R在底面四边形ABCD内(包括边界),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
平面
,
,点R到平面
的距离等于它到点D的距离,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24006d28116bc097933cc90bcc0ea69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bfb537a63ec2e7f085c0bb6eb1b2b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fa37bb4761118ea5dcb23a8de9ee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
A.点P的轨迹的长度为![]() | B.点Q的轨迹的长度为![]() |
C.PQ长度的最小值为![]() | D.PR长度的最小值为![]() |
您最近一年使用:0次
2022-04-30更新
|
1915次组卷
|
6卷引用:专题22 立体几何中的轨迹问题-1
名校
4 . 如图,已知正方体
的棱长为4,
,
分别是棱
和
的中点,
是侧面
内的动点,且
平面
,当
的外接圆面积最小时,三棱锥
的外接球的表面积为____________ .
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a53f3642feb20eee0af47001b5ffe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6b87654a4b5604ea8ca50a52adb442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5758391203b4105876f9b3f62dd054.png)
![](https://img.xkw.com/dksih/QBM/2022/3/29/2946459840069632/2948598897213440/STEM/dc58b473-b3fb-4879-9eb9-b04cc32d5c24.png?resizew=167)
您最近一年使用:0次
2022-04-01更新
|
1386次组卷
|
5卷引用:第一章 空间向量与立体几何单元测试(基础版)
名校
解题方法
5 . 如图,在棱长为1的正方体
中,P为棱
的中点,Q为正方形
内一动点(含边界),则下列说法中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/67e2df88-5a04-4e60-9457-1d2c032cc1f4.png?resizew=144)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/67e2df88-5a04-4e60-9457-1d2c032cc1f4.png?resizew=144)
A.若![]() ![]() |
B.存在Q点,使得![]() ![]() |
C.当且仅当Q点落在棱![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2022-03-23更新
|
4916次组卷
|
10卷引用:八省八校(T8联考)2022届高三下学期第二次联考数学试题
八省八校(T8联考)2022届高三下学期第二次联考数学试题江苏省南京师范大学附属中学2022-2023学年高三上学期10月月考数学试题湖南省长郡中学2023届高三下学期月考(七)数学试题广东省广州市第六中学2023-2024学年高二上学期期中数学试题河北省石家庄市正中实验中学2024届高三上学期月考(四)数学试题(已下线)空间向量与立体几何山东省济宁市汶上县第一中学2022-2023学年高三上学期12月月考数学试题浙江省温州市苍南县金乡卫城中学2022-2023学年高二下学期3月第一次月考数学试题江苏省淮安市六校联盟2022-2023学年高二下学期5月学情调查数学试题福建省漳州市第三中学2022-2023学年高二下学期期中数学试题
名校
解题方法
6 . 如图,四棱锥
中,
是等边三角形,底面
是直角梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645c2acbf5a03068cba4d6dff6563976.png)
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/11/2870313655083008/2875145049554944/STEM/7aa1701bd041479fa2643d9c8faf3b4e.png?resizew=266)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
平面
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645c2acbf5a03068cba4d6dff6563976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96fac11d72f72c805dbddb8da72d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62794ea73abc2a84aa0512c5b205eb12.png)
![](https://img.xkw.com/dksih/QBM/2021/12/11/2870313655083008/2875145049554944/STEM/7aa1701bd041479fa2643d9c8faf3b4e.png?resizew=266)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be41b05e11ba5eadaaed9a224b949774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2014·北京朝阳·二模
名校
7 . 如图,在四棱锥
中,底面
是正方形,侧面
底面
,
,
分别为
中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/d501d3cb-322e-4c1f-9add-5a4e116a7a08.png?resizew=261)
(1)求证:
平面
;
(2)求二面角
的余弦值;
(3)在棱
上是否存在一点
,使
平面
?若存在,指出点
的位置;若不存在,说明理由.
![](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/93edc7bb513f40a89173121c8570cd65.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e87d4d9a3b0f961483bf4f68be9c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931bbffda5e872703c9947eccc47ede2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/d501d3cb-322e-4c1f-9add-5a4e116a7a08.png?resizew=261)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38675b96e9409217b9e8ec34b80fff35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af558cc6819fc74127be2933360fd40.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36148e5b0d89ba45bd98b91da00bf2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14af6bf74442941c372bb708bcdcb5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2021-11-01更新
|
4050次组卷
|
12卷引用:2014届北京市朝阳二模理科数学试卷
(已下线)2014届北京市朝阳二模理科数学试卷【全国百强校】新疆乌鲁木齐市第七十中学2018-2019学年高二下学期第一次月考数学(理)试题辽宁省沈阳市郊联体2019-2020学年高二上学期期末考试数学试题天津市耀华中学2020-2021学年高二(上)第一次段考数学试题辽宁省沈阳五中2020-2021学年高二10月份月考数学试题天津市静海区大邱庄中学2021-2022学年高二上学期第一次诊断性检测数学试题(已下线)2021年新高考北京数学高考真题变式题16-21题(已下线)考点35 立体几何中的综合问题-备战2022年高考数学典型试题解读与变式(已下线)专题20 立体几何综合大题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)理科数学-2022年高考押题预测卷02(全国甲卷)(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)天津市滨海新区塘沽紫云中学2023-2024学年高二上学期第一次月考数学试题
名校
8 . 在四棱锥
中,
为等边三角形,
,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/4c468772-4545-427d-80f7-0acc2356e067.png?resizew=198)
(1)求证:
平面
;
(2)已知平面
平面
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32450995497b9e341be832e9efad3114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ad161a2674d823247f0d8236cae1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/4c468772-4545-427d-80f7-0acc2356e067.png?resizew=198)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5a2f5f4970ab8a1303523e23c8b24a.png)
您最近一年使用:0次
2021-10-09更新
|
1522次组卷
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5卷引用:广东省广州市华南师范大学附属中学2023届高三上学期第一次月考数学试题
名校
9 . 如图,在棱长为1的正方体
中,P是
上的动点,则( )
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A.直线![]() ![]() |
B.![]() ![]() |
C.![]() |
D.当P与![]() ![]() ![]() |
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8卷引用:广东省广州市三校联考2021-2022学年高一下学期期中数学试题
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解题方法
10 . 如图所示四棱锥
,底面
为直角梯形,
,
,
,
,
面
,
平面
,则
点轨迹长度为________ .
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e2a767469a06eb893169a9f3c47a1c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/396bea5c-23b1-405f-877b-881f9b30646f.png?resizew=206)
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5卷引用:重庆市南开中学校2020-2021学年高一下学期期中数学试题
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