如图①,在梯形ABCD中
,四边形ABCE是边长为2的正方形,O是AC与BE的交点将△ABE沿BE折起到△PBE的位置,使得平面PBE⊥平面BCDE,如图②.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975700215357440/2976460194807808/STEM/a3412802-f860-4a29-b457-b3c1be8452ce.png?resizew=399)
(1)求证:OC⊥平面PBE;
(2)求直线PB与平面PCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975700215357440/2976460194807808/STEM/a3412802-f860-4a29-b457-b3c1be8452ce.png?resizew=399)
(1)求证:OC⊥平面PBE;
(2)求直线PB与平面PCD所成角的正弦值.
更新时间:2022-05-10 16:46:40
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【知识点】 空间向量与立体几何综合
相似题推荐
解答题-问答题
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解题方法
【推荐1】如图,已知平行六面体
中,底面
是边长为2的正方形,
,
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32892bd69becbeaf4c18f0874e981fbe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/6a114a04-0e09-4c99-97c4-20118d055be8.png?resizew=248)
(1)用
表示
,并求
;
(2)求AC1与BD所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c47b3e7435856bedf495e1e859be631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6ed75fc5022a5d53bf64ec481dfe73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32892bd69becbeaf4c18f0874e981fbe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/6a114a04-0e09-4c99-97c4-20118d055be8.png?resizew=248)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d189ba56ed46476376bb15266540cfef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4feafb6ff8a0f0ea0fe6d3b55eb499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db065ca9e06774313be2ba4a6e39280.png)
(2)求AC1与BD所成角的大小.
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解答题-问答题
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适中
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【推荐2】如图,两条异面直线a,b所成的角为
,在直线a,b上分别取点
,E和点A,F,使
,且
.已知
,
,
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8df14d11c6f036b3b248544b731ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd72669c08e98a92cdfb9bc167ac56bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d3a1fa6db6ae6cf48884a2a30f3300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269739b055ce69fe8731dd1fd2590d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48794f1646f9f5108a7a7c445af7e9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
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解答题-证明题
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(0.65)
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【推荐3】如图,在四棱台
中,底面
为矩形,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/dedd57f5-edc7-4b86-8150-ba5e12922bbc.png?resizew=172)
(1)求证:
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384ffa4e596b6c7b8e270217a47f7227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6503add5811927fc11d86f2174f79f1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/dedd57f5-edc7-4b86-8150-ba5e12922bbc.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e076e68ef7bab94a6aba990f83159f51.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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