名校
1 . 如图,已知在四棱锥
中,底面
为等腰梯形,
,
,
为棱
上一点,
与
交于点
,且
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/7/10/2761104794034176/2762194789007360/STEM/abf8cf64da0f45ab98fbfdb4e0ae9345.png?resizew=308)
(1)证明:
;
(2)是否存在点
,使二面角
的余弦值为
?若存在,求出
点位置,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37a4845312db03260e9987b70467987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e697f29fdbcb8bd70b4294a45d3e3c.png)
![](https://img.xkw.com/dksih/QBM/2021/7/10/2761104794034176/2762194789007360/STEM/abf8cf64da0f45ab98fbfdb4e0ae9345.png?resizew=308)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9becfe76ad584897860dc957da44219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2404f102217c8d5a6ee46a92b5fc40de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2021-07-11更新
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