如图,正方体
的棱长为1,P为侧面
(含边界)内的动点,若直线
与
的夹角为
,则下列说法正确的是______
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/0b17ddf8-a5a2-424e-a3e2-965fd6286bb8.png?resizew=183)
①点P的运动轨迹的长度为
,
②
的长度为定值
③当CP最小时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f669842930533006b4bd7921f2f41a.png)
④存在点P,使得直线
和平面
所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/0b17ddf8-a5a2-424e-a3e2-965fd6286bb8.png?resizew=183)
①点P的运动轨迹的长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
③当CP最小时,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a00da93b82b518094c4abdc19253022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f669842930533006b4bd7921f2f41a.png)
④存在点P,使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22ebcc4aa98d46366df48f751a5f368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
更新时间:2023-10-11 07:07:35
|
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【推荐1】如图,正方体
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【推荐1】在棱长为2的正方体
中,
分别为
的中点,点
在底面
内,若直线
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