如图,在正方体
中,点
是对角线
上一动点,在点
从顶点
移动到顶点
的过程中,下列结论中错误的有( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/dc255631-7e3a-4fd5-b381-b5abfe53f6e5.png?resizew=172)
![](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/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/dc255631-7e3a-4fd5-b381-b5abfe53f6e5.png?resizew=172)
A.二面角![]() ![]() |
B.直线![]() ![]() |
C.存在一个位置,使得![]() ![]() |
D.存在一个位置,使得平面![]() ![]() |
更新时间:2022-12-26 20:40:12
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解题方法
【推荐1】如图,在棱长为1的正方体
中,点
分别在线段
和
上.给出下列四个结论中所有正确结论的个数有( )个
①
的最小值为1
②四面体
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
③存在无数条直线
与
垂直
④点
为所在边中点时,四面体
的外接球半径为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/15/c7b0224a-dbc8-41fb-865b-058fdbd9264f.png?resizew=155)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb1d7bd70e898d08f78de751294df1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
③存在无数条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
④点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb1d7bd70e898d08f78de751294df1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
A.1 | B.2 | C.3 | D.4 |
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【推荐2】在棱长为2的正方体
中,点
,
分别是棱
,
的中点,动点
在正方形
(包括边界)内运动.若
平面
,则
的最小值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/b00d4bea-3079-4280-aa89-f7b4e1dd61a8.png?resizew=180)
![](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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c49036a80d4ce30770ba36958838b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/b00d4bea-3079-4280-aa89-f7b4e1dd61a8.png?resizew=180)
A.2 | B.![]() | C.![]() | D.![]() |
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【推荐1】已知
是半径为6的球
表面上的三个点,且
,则三棱锥
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba919d5c415b91dbf2c78142ab01714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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【推荐2】如图所示,在长方体中,
,点
是棱
上的一个动点,平面
交棱
于点
,下列命题错误的是( )
A.四棱锥![]() |
B.存在点![]() ![]() ![]() |
C.存在唯一的点![]() ![]() |
D.对于棱![]() ![]() ![]() ![]() ![]() ![]() |
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【推荐1】动点
在正方体
从点
开始沿表面运动,且与平面
的距离保持不变,则动直线
与平面
所成角正弦值的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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【推荐2】如图,线段AB在平面
内,线段
,线段
,且
,
,
,则直线CD与平面
所成角的正弦值为( )
![](https://img.xkw.com/dksih/QBM/2021/1/22/2641672120852480/2643138693308416/STEM/61cad6b3-d8e1-4dc2-900c-f56fcd27ad79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8089ef4b9af6a9c54fb8316837aee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b455b110a30c1533d0a0657e0e48ac33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e0c5cb53fd85b7a23f0580df6bb49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dee72ac866c7fc89bcabe7cc484944e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a7fcbeecd5572cbc2c65f220ec03df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/2021/1/22/2641672120852480/2643138693308416/STEM/61cad6b3-d8e1-4dc2-900c-f56fcd27ad79.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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【推荐1】如图,已知三棱锥D-ABC,
,
,记平面DAB,平面DBC,平面DAC与底面ABC所成的锐二面角分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f2325b9ff04ca24e29be9dfe11f9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e0a065197a8dd7bc931f73fe1ea27a.png)
,则( )
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445374506565632/2445660921520128/STEM/a62cc4223a3c4dd18b8b6724b7d64a4e.png?resizew=200)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc21ea7ca5f3efb35eccf8d3d1acb10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f2325b9ff04ca24e29be9dfe11f9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e0a065197a8dd7bc931f73fe1ea27a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
![](https://img.xkw.com/dksih/QBM/2020/4/20/2445374506565632/2445660921520128/STEM/a62cc4223a3c4dd18b8b6724b7d64a4e.png?resizew=200)
A.![]() | B.![]() | C.![]() | D.![]() |
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【推荐2】如图,在三棱柱
中,点
在平面
内运动,使得二面角
的平面角与二面角
的平面角互余,则点
的轨迹是
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/96cd0cea-5f23-4e81-8d2f-06c6a9bc9073.png?resizew=135)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/96cd0cea-5f23-4e81-8d2f-06c6a9bc9073.png?resizew=135)
A.一段圆弧 | B.椭圆的一部分 |
C.抛物线 | D.双曲线的一支 |
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