1 . 已知平面
经过三点
,求平面
的一个法向量是_________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8476f6d7b0bb1ef364ecff5fc21737e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2 . 如图:在长方体
中,
,
,建立如图所示的空间直角坐标系,则下列向量是平面
的一个法向量的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/94264093-5b73-45e5-9f8c-28d2e3f30d25.png?resizew=224)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1b292baa30ffc34df3a47d57b60c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5282adc6d7e3cf2162d380a3e0b882ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044694e9cf35c029509360dc556a8afb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/94264093-5b73-45e5-9f8c-28d2e3f30d25.png?resizew=224)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 如图,在直四棱柱
中,底面
是平行四边形,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/c655e790-149a-411f-99df-e4edc129dbe2.png?resizew=186)
(1)求证:
;
(2)在线段
上是否存在点
,使得
平面
?若存在,求
的值;若不存在,说明理由.
![](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/606c6e9fb76e8cab206af9bfd3030dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e93d4e968f0d173491cc2834a3c99de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/c655e790-149a-411f-99df-e4edc129dbe2.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c00b2c1b65436a95cb02b12f80df57e.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95bd4a189362c68e646bb13745b7d6b.png)
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4 . 如图,已知
为正方形,
平面
,
,且
,
为
与
的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/539cb464-7713-45b7-bb26-e5e1b9f69978.png?resizew=250)
(1)求证:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e1ab3840f34df7791e037f8e668533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f48b46f0238bf1f3635e3488ad7687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834c73d2066414ea2a84479b3eb60731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/539cb464-7713-45b7-bb26-e5e1b9f69978.png?resizew=250)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42179325557ca0fe1e903baf2c5dea5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae32d0e1180c74ef27840cb642d4c38.png)
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5 . 如图在边长是
的正方体
中,
,
分别为
,
的中点.应用空间向量方法求解下列问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/9fe6468a-743a-4379-a4a0-2f7dd7930638.png?resizew=263)
(1)证明:
平面
;
(2)证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9880952857950577055578875ab29141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7ddbb49c644bf06ccbad885ba2c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475e6a90dcd426d7c88b83f9e20e6578.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/9fe6468a-743a-4379-a4a0-2f7dd7930638.png?resizew=263)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119443fa34dbcd836ad231f727600afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f563e440c2400574de49eb063c46a065.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92dc7c262bba52d1b97c17c6d07e9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6610370a5aefaf45fdb579521484e3b5.png)
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2022-10-24更新
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2卷引用:吉林省吉林市蛟河市第二高级中学校2022-2023学年高二上学期期中数学试题
6 . 已知空间中两条不同的直线
,两个不同的平面
,则下列说法中错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ccc19a183b9ce7f82d2609a14b9a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe681f962c3dfcbd0508bbd66107d16.png)
A.若直线![]() ![]() ![]() ![]() ![]() ![]() |
B.若直线![]() ![]() ![]() ![]() ![]() ![]() |
C.若平面![]() ![]() ![]() ![]() ![]() |
D.若平面![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 . 如图,圆的直径
,
为圆周上异于
的点,
垂直于圆所在平面,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/51fbea9f-9968-4225-8a96-4f4c4e28bcde.png?resizew=137)
(1)求证:
;
(2)若
,求平面BCP与平面ACP夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494529576e5b2b25074fcc7986c52a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a051702dc3c9f71e25dec5abdd614426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732c37c8318f805314d51134d075cb4b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/51fbea9f-9968-4225-8a96-4f4c4e28bcde.png?resizew=137)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c209827e914ab17f5bc2e6fab044a05.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f485914f6918545a5209d4785c369a4d.png)
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8 . 已知空间中三点
,
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf215bb6e25e2250c8f9af7f0b6beb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6e841fe08205253077debef9d8815d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7467f6cc22d543fd960299a5ad20e24.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() ![]() | D.平面![]() ![]() |
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9卷引用:第08讲 空间向量及其运算的坐标表示 -【暑假自学课】2022年新高二数学暑假精品课(人教版2019必修第二册+选择性必修第一册)
(已下线)第08讲 空间向量及其运算的坐标表示 -【暑假自学课】2022年新高二数学暑假精品课(人教版2019必修第二册+选择性必修第一册)河南省洛阳新学道高级中学2022-2023学年高二上学期第一次月考数学试题江西省南昌市新建区第二中学2022-2023学年高二上学期10月学业水平考核数学试题山东省聊城市第二中学2022-2023学年高二上学期第一次月考数学试题黑龙江省牡丹江市第三高级中学2022-2023学年高二上学期第一次月考数学试题山东省聊城颐中外国语学校2022-2023学年高二上学期第一次月考数学试题安徽省芜湖市无为襄安中学2022-2023学年高二上学期12月月考数学试题云南省怒江州泸水市怒江新城新时代中学2022-2023学年高二上学期期中考试数学试题湖北省黄冈市蕲春县2021-2022学年高二上学期期中数学试题
名校
解题方法
9 . 在长方体
中,已知
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/67fe8b2d-bdc9-4be2-adef-f298ed2547b8.png?resizew=152)
(1)在线段
上是否存在点F,使得平面
平面
?若存在,请加以证明;若不存在,请说明理由;
(2)设
,点G在
上且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a5a1abb6d0c0a4829759ca7b8912c4.png)
,求
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7ddbb49c644bf06ccbad885ba2c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974e32fac0b8857d855464877fa071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/67fe8b2d-bdc9-4be2-adef-f298ed2547b8.png?resizew=152)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e54038fa9518fc9a3aa2cb97a74196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033d55114db68c273ab3b8b4e4b95fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88487c4c5a2ab5965089a71d8bc2377a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ea10159a3ebf75567a4c469937b8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17230625e72d3a9c6d72ff61019ff61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a5a1abb6d0c0a4829759ca7b8912c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b88e7cb71b8bad003650863e98ed306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47614ea5ee81059bf3352f38782ac00.png)
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2022-10-23更新
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11卷引用:专题04 立体几何-2021年高考真题和模拟题数学(理)专项汇编(全国通用)
(已下线)专题04 立体几何-2021年高考真题和模拟题数学(理)专项汇编(全国通用)(已下线)7.5 空间向量求空间角(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)专题8.7 立体几何中的向量方法(练)- 2022年高考数学一轮复习讲练测(新教材新高考)(已下线)专题04 立体几何-备战2022年高考数学母题题源解密(新高考版)(已下线)专题22 盘点空间线面角的问题——备战2022年高考数学二轮复习常考点专题突破浙江省金华市东阳市横店高中2022-2023学年高三上学期10月检测数学试题黑龙江省哈尔滨市第六中学校2022-2023学年高三上学期期中数学试题黑龙江省双鸭山市饶河县饶河县高级中学2022-2023学年高二上学期期中数学试题湖南省2021届高三数学模拟试题(黑卷)(已下线)考点33 直线、平面平行的判定及其性质-备战2022年高考数学(理)一轮复习考点帮(已下线)专题10 导数及其应用-备战2022年高考数学母题题源解密(新高考版)
解题方法
10 . 如图,在直棱柱
的底面
中,
,
,棱
,以
为原点,分别以
,
,
所在直线为
轴建立如图的空间直角坐标系
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/51c63b05-d662-4dcb-87ba-8b932726769e.png?resizew=177)
(1)求平面
的一个法向量;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad389858be11534828cc4090e2efa647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854f480c60b88b546cb15d3b5622e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed18681d5039e5c8f1249c44bf15847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee98db8495cf1f203abe99795102e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2a49f58140008b8f85a00f06acdffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb16f7dbc4b9993c4efa0764df1d8ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02b87b8fe02993aac5687c9d4df3b3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/51c63b05-d662-4dcb-87ba-8b932726769e.png?resizew=177)
(1)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d393149fe452850d47f3141099032ddf.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d393149fe452850d47f3141099032ddf.png)
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2022-10-22更新
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2卷引用:重庆市二0三中学校2022-2023学年高二上学期第一次月考数学试题