在正方体
中,点P满足
,其中
,
,现有如下四个命题:
①存在
,
,使得
平面
;
②当
时,
平面
;
③当
时,
与平面
所成角的最小值为
;
④若点P到直线
与到直线AD的距离相等,则点P的轨迹是线段.
其中所有真命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb447c496f455e3684b8809f0729736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231ecbf3b26a3ba1fdb7cbbd6ba90e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0518fab92475787a7be0581733eea67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da8cca18b54a2e706c83e48ba70e327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbae94f2dd5086f7ddbe18407a978e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
④若点P到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
其中所有真命题的序号是
更新时间:2023-06-14 15:26:35
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