如图,
平面
,
且
,则此三棱锥四个面中直角三角形的个数为______ ,异面直线
与
所成角的正切值等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca5bc93e35e739f6bccb8ca2003abb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2020/1/14/2376918091956224/2376969109053440/STEM/ee76107dec8c43af80a739120eb42537.png?resizew=113)
19-20高二·浙江·期末 查看更多[5]
(已下线)【新东方】杭州新东方高二数学试卷255(已下线)专题8.7 立体几何中的向量方法(精练)-2021年新高考数学一轮复习学与练(已下线)专题1.3 空间向量的应用(A卷基础篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教A版,浙江专用)广东省汕头市潮阳南侨中学2021-2022学年高二上学期第一阶段考试数学试题广东省惠来县第一中学2023-2024学年高二上学期第一次阶段考试数学试题
更新时间:2020-01-14 16:58:56
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解题方法
【推荐1】如图是正方体的平面展开图,则在这个正方体中,异面直线AB与CD的夹角为__________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/5a046fd9-edea-494e-b42f-746ef414fcfa.png?resizew=160)
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【推荐2】如图,在正方体
中,有以下结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/61f21015-f07e-4a9d-8f51-ba5029176f73.png?resizew=187)
①
平面
;
②
平面
;
③
;
④异面直线
与
所成的角为
.
则其中正确结论的序号是____ (写出所有正确结论的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/61f21015-f07e-4a9d-8f51-ba5029176f73.png?resizew=187)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb7915995a29183113fd778dabee6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa142bb96af98b846997e681609739f.png)
④异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9bf2423499d45354dbc8377f1f04e16.png)
则其中正确结论的序号是
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【推荐1】已知正方体
,点
分别是线段
和
上的动点,给出下列结论:
①对于任意给定的点
,存在点
,使得
;
②对于任意给定的点
,存在点
,使得
;
③对于任意给定的点
,存在点
,使得
;
④对于任意给定的点
,存在点
,使得
.
其中正确结论为______________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f335994a0c362bc3ddd6fa9142e9b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35fcfb721ae78f090d69a402367ede1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
①对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d83ca07fe88e9c926c9e5db3846cc9.png)
②对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d83ca07fe88e9c926c9e5db3846cc9.png)
③对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c125cc43226c9ebe2003e4f6c50bb9c.png)
④对于任意给定的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c125cc43226c9ebe2003e4f6c50bb9c.png)
其中正确结论为
![](https://img.xkw.com/dksih/QBM/2021/10/20/2833568467517440/2834718824988672/STEM/860bed1625214632a3ff79658ea1bfa7.png?resizew=142)
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【推荐2】如图,正三角形ABC的边长为2,P是三角形ABC所在平面外一点,
平面ABC,且
,则P到BC的距离为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://img.xkw.com/dksih/QBM/2021/11/15/2851928473346048/2853475952099328/STEM/566da4f3-d644-4cfe-9ebb-6972a905a24e.png)
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【推荐1】在正方体ABCD-A1B1C1D1中,P为棱AB的中点,则直线A1P与BC1所成角为
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【推荐2】直三棱柱
中,
,
则异面直线
和
所成角的余弦值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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【推荐3】如图,在直角梯形
中,
,过点A作
交SC于点D,以AD为折痕把
折起,当几何体
的的体积最大时,则下列命题中不正确的是___________ (写出所有假命题的序号).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3ee488ae-83b9-4810-aff8-c77285190465.png?resizew=185)
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa715d27ae43ec1e157226bc9dea54.png)
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
③SA与平面
所成的角等于SC与平面
所成的角
④AB与SC所成的角等于DC与SA所成的角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334a5773c8d24f29ec3231075170e4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3beeda94d1247c045e62a9b93965d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39043732454c9364dca44f7f59640121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5830322dd2824ed012a68f1a2bd9c742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3ee488ae-83b9-4810-aff8-c77285190465.png?resizew=185)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa715d27ae43ec1e157226bc9dea54.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
③SA与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
④AB与SC所成的角等于DC与SA所成的角
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