1 . 如图,在棱长为1的正方体
中,
是棱
上的一个动点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
A.棱锥![]() | B.截面![]() ![]() |
C.存在点![]() ![]() ![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
2023-07-12更新
|
320次组卷
|
2卷引用:湖北省荆门市2022-2023学年高一下学期期末数学试题
名校
2 . 如图,在棱长为2的正方体
中,
是
的中点,
![](https://img.xkw.com/dksih/QBM/2021/4/11/2697654008971264/2824133951291392/STEM/1e030125bdb9447a973fc55b22e196df.png?resizew=254)
(1)求直线
与平面
所成角的余弦值;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2021/4/11/2697654008971264/2824133951291392/STEM/1e030125bdb9447a973fc55b22e196df.png?resizew=254)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11990928efcd42ebe7a82a5f1105a708.png)
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3 . 如图,已知
是边长为4的正三角形,D,E分别为AC,AB的中点,把
沿DE折起,使点A到达点P的位置,且平面PDE
平面BCDE.
![](https://img.xkw.com/dksih/QBM/2020/9/7/2544627511353344/2544878578188288/STEM/231e7455-c1c3-4699-a0ca-14dc65ce960c.png?resizew=401)
(1)求PB与平面BCDE所成角的正弦值;
(2)求点E到平面PBC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460edcced5597615113c0fdc95b1dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://img.xkw.com/dksih/QBM/2020/9/7/2544627511353344/2544878578188288/STEM/231e7455-c1c3-4699-a0ca-14dc65ce960c.png?resizew=401)
(1)求PB与平面BCDE所成角的正弦值;
(2)求点E到平面PBC的距离.
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名校
解题方法
4 . 已知三棱柱
的底面是正三角形,侧面
为菱形,且
,平面
平面
,
、
分别是
、
的中点.
![](https://img.xkw.com/dksih/QBM/2020/3/19/2423138566766592/2423630358208512/STEM/05a2608adae7431da5b603bf448c3633.png?resizew=217)
(1)求证:
平面
;
(2)求证:
;
(3)求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2020/3/19/2423138566766592/2423630358208512/STEM/05a2608adae7431da5b603bf448c3633.png?resizew=217)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9aa113258bfa138c95a621f64fc74.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
2020-03-20更新
|
662次组卷
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4卷引用:湖北省荆门市2018-2019学年高一下学期期末数学试题
5 . 已知正三棱柱ABC-A1B1C1的体积为
,底面是边长为
的正三角形.若P为△A1B1C1的中心,则PA与平面ABC所成角的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdcce9914d42ab1dc31be3f62b1bec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f8c3ba00c59e0634ed10fa85289de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2018-01-10更新
|
280次组卷
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2卷引用:2014-2015学年湖北省荆门市高一下学期期末质量检测数学试卷
12-13高二上·陕西西安·期末
解题方法
6 . 如图,在长方体ABCD-A1B1C1D1中,AB=BC=2,AA1=1,则AC1与平面A1B1C1D1所成角的正弦值为________ .
![](https://img.xkw.com/dksih/QBM/2012/8/30/1570992182132736/1570992187211776/STEM/8da9a222-e858-44e8-80e3-385a2306d002.png)
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