名校
1 . 已知正方体
的棱长为2,E,F分别是棱
,
的中点,P为底面ABCD内(包括边界)一动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
A.若直线![]() ![]() ![]() |
B.若![]() ![]() |
C.二面角B—EF—D的正切值为![]() |
D.过E,F,C的平面截该正方体所得截面为五边形 |
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2023-07-05更新
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658次组卷
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6卷引用:新疆维吾尔自治区可克达拉市兵团地州学校2022-2023学年高一下学期期末联考数学试题
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名校
解题方法
2 . 如图,长方体
中,
,
,
,点
是侧面
上的一个动点(含边界),
是棱
的中点,则下列结论正确的是________
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/55af4c7c-3944-4306-a5dc-0157e6b648b5.png?resizew=131)
①当
长度最小时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②当
长度最大时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
③若保持
,则点
在侧面内运动路径的长度为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
④若
在平面
内运动,且
,则点
的轨迹为圆弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/55af4c7c-3944-4306-a5dc-0157e6b648b5.png?resizew=131)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06f5fe37478ba1c140b2bc90e13d7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06f5fe37478ba1c140b2bc90e13d7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
③若保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90dd18184d12e9c1d8d1fca40973166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd11ad586fb5b7a29d22b69c89ef5bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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