解题方法
1 . 空间中有一个平面
和两条直线m,n,其中m,n与
的交点分别为A,B,
,设直线m与n之间的夹角为
,
距离的最大值;
(2)如图2,若直线m,n互为异面直线,直线m上一点P和直线n上一点Q满足
,
且
,
(i)求直线m,n与平面
的夹角之和;
(ii)设
,求点P到平面
距离的最大值关于d的函数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)如图2,若直线m,n互为异面直线,直线m上一点P和直线n上一点Q满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c1ad40967e9c203bbc1cb3044a8f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d76944a4c4cd915a11387bde580f317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c50360563e2a58800af3a9cf7d9652.png)
(i)求直线m,n与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d41f02556e958e7f0ae5e75798b33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5297dae46e09a5e0e870e29cef56c14a.png)
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2 . 坐落于武汉市江汉区的汉口东正教堂是中国南方唯一的拜占庭式建筑,象征着中西文化的有机融合.拜占庭建筑创造了将穹顶支承于独立方柱上的结构方法和与之相呼应的集中式建筑形制,其主体部分由一圆柱与其上方一半球所构成,如图所示.其中
是下底面圆心,
是
上三点,
是上底面对应的三点.且
共线,
,
,
,
与
所成角的余弦值为
.
![](https://img.xkw.com/dksih/QBM/2022/4/5/2951709161218048/2952814578597888/STEM/38eb06fb4510489bbacc181ff8a07daf.png?resizew=170)
(1)若
到平面
的距离为
,求
的半径.
(2)在(1)的条件下,已知
为半球面上的动点,且
,求
点轨迹在球面上围成的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2c4f20594ab1443c0d8dcce42895f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13510a1a5415032a5ab8f8ab911d159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464e16e3387532eb66521b4e97791cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47f25ebba1f114b54f2bf94d2f57405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9d2edbfe20c8426ba1f2a06fc178ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd0cecf5c102254b9755e42a80c3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08493c1e001d85731cb4863ec38857fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae0be5ae2bc3648d69fdc3f27be6a8f.png)
![](https://img.xkw.com/dksih/QBM/2022/4/5/2951709161218048/2952814578597888/STEM/38eb06fb4510489bbacc181ff8a07daf.png?resizew=170)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)在(1)的条件下,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9e7fb43caa87908b8d17c56e873fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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