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1 . 在棱长为1的正方体A1B1C1D1-ABCD中,M为底面ABCD的中心,Q是棱A1D1上一点,且
,∈[0,1],N为线段AQ的中点,给出下列命题:
①CN与QM共面;
②三棱锥A-DMN的体积跟的取值无关;
③当
时,AM⊥QM;
④当
时,过A,Q,M三点的平面截正方体所得截面的周长为
.
其中正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/6/2973473594449920/2979117701652480/STEM/3d648aa9-e7a2-40c5-aa90-5231d330babd.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43a2f5f1f2c76f8fe090ec8a208682c.png)
①CN与QM共面;
②三棱锥A-DMN的体积跟的取值无关;
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f83464bf17f9d4d9ee6a7f299539871.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4f6553b387f1576e4718bf60b601b4.png)
其中正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/6/2973473594449920/2979117701652480/STEM/3d648aa9-e7a2-40c5-aa90-5231d330babd.png?resizew=165)
A.①②③ | B.①②④ | C.①③④ | D.②③④ |
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解题方法
2 . 如图,平面四边形
中,
是等边三角形,
且
是
的中点.沿
将
翻折,折成三棱锥
,翻折过程中下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303653896192/STEM/3445b240-0268-42df-a6a4-92ec57df03e6.png?resizew=403)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8915e8e775538d41debf1933102c6b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ed50d0d07c007195a0263a57adbf3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303653896192/STEM/3445b240-0268-42df-a6a4-92ec57df03e6.png?resizew=403)
A.存在某个位置,使得![]() ![]() |
B.棱![]() ![]() ![]() ![]() ![]() |
C.当三棱锥![]() ![]() |
D.当二面角![]() ![]() ![]() |
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3 .
,
分别为菱形
的边
,
的中点,将菱形沿对角线
折起,使点
不在平面
内,则在翻折过程中,下列选项正确的是( )
①
平面
;②异面直线
与
所成的角为定值;③在二面角
逐渐变小的过程中,三棱锥
外接球的半径先变小后变大;④若存在某个位置,使得直线
与直线
垂直,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/13/c94f3cdc-eca0-497e-ad0f-424a7aa8b625.png?resizew=339)
![](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/411b38a18046fea8e9fab1f9f9b80a5f.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/13/c94f3cdc-eca0-497e-ad0f-424a7aa8b625.png?resizew=339)
A.①② | B.①②④ | C.①④ | D.①②③④ |
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4 . 在正方体
中,E是侧面
内的动点,且
平面
,则直线
与直线AB所成角的正弦值的最小值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/c91bc638-e93f-400d-9cab-c5f030944d23.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3490f2c22393e71edfbf594f6b3203b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5798b91907330ca16e1c894e9347cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca4606ba33e0d2d258c40660d24ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb4c5388b7cee5a7fc9c6a503447222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288ef5f0ba23ceed33b60d8685839c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/c91bc638-e93f-400d-9cab-c5f030944d23.png?resizew=168)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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