名校
1 . 如图,已知三棱柱
的侧棱与底面垂直,
.
分别是
的中点,点
在直线
上,且
.
;
(2)当
取何值时,直线
与平面
所成角
最大?并求该角取最大值时的正切值.
(3)是否存在点
,使得平面
与平面
所成的二面角的正弦值为
,若存在,试确定点
的位置,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28faa4fb5ac3c67813387512534cbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6429a01a3c89200d73dc49bd70c2d08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597362da92c667625827a89c1c2e3dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4ece75fe9b8555909be5a00d2b7af0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
2 . 已知三棱柱
中,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6801195118dbf276b001b56ade179fe4.png)
平面
;
(2)若
,且P是AC的中点,求平面
和平面
的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df209c58c4cc146ef62100e6d3b068d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6801195118dbf276b001b56ade179fe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1752434352ecb9834eaba9c63fc9abe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
您最近一年使用:0次
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3 . 已知向量
,
,
.
(1)当
时,若向量
与
垂直,求实数
的值;
(2)若向量
与向量
,
共面,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d5da9382667d04559003325bc360fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e75574d292e3db85d3edfb1be470c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5be8ab25e1c473bf8f729210f0811a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5594493362619a74d98d4aedccd6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652e029f2a9d029c5f2d2e1407cb26a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d8e782e9687f2e6276a8541ff8dcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d8e782e9687f2e6276a8541ff8dcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff409cd3886c767afb13c9a869c5f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6570cd7c2f81c9fcffd2c64664f1564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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解题方法
4 . 已知椭圆
经过
和
,
分别为椭圆的左顶点、右顶点、上顶点.
(1)求椭圆
的标准方程;
(2)过
轴上点
(点
在椭圆
长轴上)作直线交椭圆
两点,且
,若
,求
点的坐标;
(3)过点
作直线交椭圆
于
点,交直线
于
,直线
于
轴相交于
,求证:
为定值,并求此定值.(其中
分别为直线
和直线l,
的斜率).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1bbd2face8220cbd14191212588aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2314fc922502d8fc6d13e4b9f2775b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd07fb0b22450681d23d5f0513d8e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94e87c1ed4c9c0cd0f9e1f10f11a35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21791b26a0b406302709f9776dd9f28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4849d0599bbeaccc05eb0cece91ec97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eacfcd9c21fffe2820a00dd4f09ef25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
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5 . 如图,已知四棱台
的上、下底面分别是边长为2和4的正方形,平面
平面
,
,点
是棱
的中点,点
在棱
上.
点在什么位置时,使得
平面
;
(2)若面
与面
所成角的正弦值为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b90595662af9a1936e1e703462cb69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b35708245a5da381178284f5ac7ce9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e631a0a91c5c85bce742209159e5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
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6 . 如图,在四棱锥
中,平面
平面
,
,
且
,
,
,
,
,
为
的中点.
平面
;
(2)求平面
与平面
所成锐二面角的余弦值;
(3)在线段
上是否存在一点
,使得直线
与平面
所成角的正弦值为
,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250833a6c405ffd724b673b478c22919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585a36dc7fe184aa99338bb2ecf1b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874470622cffc5704671f9bf700ace38.png)
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2024-04-29更新
|
602次组卷
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2卷引用:江苏省盐城市五校联盟2023-2024学年高二下学期4月期中考试数学试题
名校
7 . 如图,在四棱锥
中,四边形
为梯形,其中
,
,
,平面
平面
.
;
(2)若
,且
与平面
所成角的正切值为2,求平面
与平面
所成二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2d5ab801f2a84b78139b0ea2c5032b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8e49d68afab33806a63d25a0861c7c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
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2024-04-24更新
|
1290次组卷
|
3卷引用:江苏省盐城市东台市安丰中学等六校2024届高三下学期4月联考数学试题
江苏省盐城市东台市安丰中学等六校2024届高三下学期4月联考数学试题福建省莆田第一中学2023-2024学年高二下学期3月月考数学试卷(已下线)模型3 用定量+定性双法分析立体几何中的求角问题模型(高中数学模型大归纳)
名校
8 . 已知向量
,O为坐标原点,点
.
(1)求
;
(2)若点E在直线AB上,且
,求点E的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5bbf65384f71bd6a5b672dc4001c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e2403c664d630716fb653a303f556a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16111d1425b87ba82ea6a706d1dfb3ef.png)
(2)若点E在直线AB上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9703b7ec9840ddec5449aa68e5cfecf5.png)
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2024-04-13更新
|
262次组卷
|
6卷引用:江苏省盐城市五校联考2023-2024学年高二下学期第一次学情调研检测(3月)数学试题
江苏省盐城市五校联考2023-2024学年高二下学期第一次学情调研检测(3月)数学试题(已下线)专题12 空间向量的坐标表示8种常见考法归类-【寒假自学课】2024年高二数学寒假提升学与练(苏教版2019)甘肃省白银市会宁县第四中学2023-2024学年高二下学期第一次月考数学试卷福建省平山中学、内坑中学、磁灶中学、永春二中、永和中学2023-2024学年高二上学期期中联考数学试题福建省泉州市泉州九中与侨光中学2023-2024学年高二上学期12月联考数学试题(已下线)模块一 专题1 空间向量的基本运算 B提升卷 期末终极研习室(2023-2024学年第一学期)高二人教A版
名校
解题方法
9 . 对于实数,
,
,
,称
为二阶行列式,定义其一种运算:
.对于向量
,
,称
为
与
的向量积,定义一种运算:
.在三棱锥
中,已知
,
,
,
.
(1)试计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a8581d5e7ca88c3ce1c8d4057263db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667118b4717faeba287c908bd0bd33ec.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(3)求三棱锥的侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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解题方法
10 . 已知椭圆C:
,
,过P点斜率为k的直线与椭圆C交于另一点为Q.
(1)若
的面积为
,求k的值;
(2)若直线
与椭圆C交于M,N两点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0bffbc252b3abcacfbd0cce9df263f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc762dc0fe9038201284106554f59cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edec6bc820d2fab581cdc0d9af5d30f1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a4a7f7496bf126a583563799a43f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36631fe9e7ac2ad233a065b928b98dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-27更新
|
429次组卷
|
2卷引用:江苏省射阳中学2023-2024学年高二下学期3月阶段测试数学试题