名校
解题方法
1 . 正方体
的棱长为4,
,
分别为棱
,
的中点,过
,
,
做该正方体的截面,则截面形状为___________ ,二面角
的平面角的余弦值为___________ .
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](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/4e7be2f695260a14809dec7d84dfd6fc.png)
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名校
解题方法
2 . 在直四棱柱
中,底面为矩形,
,
分别为底面的中心和
的中点,连接
.
平面
;
(2)若
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5098d4c7c2f093aa91003afd3602e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e7f10e0c8af2d0d02a685f6f19e329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187b7264a14c630a8ea1d13cad403bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b508e5a78733e4bb60265b844019c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed6781a17fd88de5abf88f225894e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b14cf4977ee2dac0bd5b0fca4dadc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f59727be34cd56e46ede26aa3c0cf1.png)
您最近一年使用:0次
2024-04-12更新
|
449次组卷
|
3卷引用:江苏省盐城中学2023-2024学年高二下学期5月阶段性质量检测数学试题
名校
解题方法
3 . 如图,八面体
的每一个面都是边长为4的正三角形,且顶点
在同一个平面内.若点
在四边形
内(包含边界)运动,
为
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2c288fabe405ad5ee7c5e4b448d0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
A.当![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.存在一个体积为![]() ![]() |
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2024-04-02更新
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412次组卷
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5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
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4 . 若平面
外的直线
的方向向量为
,平面
的法向量为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d09dd7ad583bce7523952f10580009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b150d42f3c6324cdbb22582df50d6b.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
您最近一年使用:0次
2024-04-02更新
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443次组卷
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3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
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5 . 如图,在四棱锥
中,底面
为平行四边形,
,
,
底面
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/60b4b2a6-ae75-453f-8a56-f44b24dae14d.png?resizew=191)
![](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/3cf80b036459da6dcb841a4bbe3859fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88867f687e53d643968e06567e3a6556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/60b4b2a6-ae75-453f-8a56-f44b24dae14d.png?resizew=191)
A.点A到平面![]() |
B.![]() ![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.二面角![]() ![]() |
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名校
解题方法
6 . 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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7 . 如图,在四棱锥
中,
平面
,
,
,
是等边三角形,
为
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
平面
;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a301baf6cc0628366e6661a87a2d93ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19f0fcacac715a1200770516d1e4a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2024-03-27更新
|
507次组卷
|
2卷引用:江苏省盐城市2023-2024学年高二下学期5月月考数学试题
名校
解题方法
8 . 如图,在四棱锥
中,平面
平面ABCD,
,
,M为棱PC的中点.
平面PAD;
(2)若
,
(i)求二面角
的余弦值;
(ii)在线段PA上是否存在点Q,使得点Q到平面BDM的距离是
?若存在,求出PQ的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be80fe6e1bdcd8f7ac98afaaff031530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c098151bc644ca1eda2a76032927f82d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f2acab56e2002173333e27b5738416.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c651b55c0ad7f63e3451557ab4c378be.png)
(i)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678bd649fc4c7e780f785e2fc704bd89.png)
(ii)在线段PA上是否存在点Q,使得点Q到平面BDM的距离是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c76e558109d9b8dd700c1a7f9cc73ad.png)
您最近一年使用:0次
2024-03-21更新
|
1397次组卷
|
7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)数学试题湖南省常德市汉寿县第一中学2023-2024学年高二下学期3月月考数学试题上海市格致中学2023-2024学年高二下学期期中考试数学试题福建省莆田第二十五中学2023-2024学年高二下学期期中考试数学试题(已下线)专题03 空间向量及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)(已下线)专题03空间向量及其应用--高二期末考点大串讲(沪教版2020选修)
名校
解题方法
9 . 已知点
,若点
和点
在直线
上,则点
到直线
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64734d55f546a85299a29e4bedef2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae566e8eb2a4eca4e1cad9f5b99289f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12514037920d9f9ed3cf485a581848d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-17更新
|
321次组卷
|
2卷引用:江苏省盐城中学2023-2024学年高二下学期5月阶段性质量检测数学试题
10 . 如图,多面体
中,底面
为菱形,
,
平面
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/1a8c5b06-82a4-4ddd-9b7a-81640ff8f2cc.png?resizew=157)
(1)求证:
平面
;
(2)求二面角
的余弦值的绝对值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1d3de310412c0fa445acd2cdb61513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96ea447e633f7165fa4944be69a3f62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/1a8c5b06-82a4-4ddd-9b7a-81640ff8f2cc.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f70cf3f6c7acbf60d4a4ca0ce89619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a34e44c5d7e1d22521fb293994f5b0.png)
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