名校
1 . 如图,在菱形
中,
,
,将
沿对角线
翻折到
位置,连接
,构成三棱锥
.设直线
和直线
所成角为
.
(1)求证:
;
(2)当
取最小值时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/31/9a5f9045-5a46-44ee-a3d0-14791763be33.png?resizew=347)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
您最近一年使用:0次
名校
2 . 如图,在正三棱柱
中,底面边长为2,
,D为
的中点,点E在棱
上,且
,点P为线段
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/2be24535-d23a-4661-b2af-064d6ac435b2.png?resizew=162)
(1)求证:
;
(2)若直线
与
所成角的余弦值为
,求平面
和平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97f616f0f32beed421129cbbb4db8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8feb05b8c76753d5bd053f254085cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/2be24535-d23a-4661-b2af-064d6ac435b2.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bdc76aa57c179e3164049ca9fe17533.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466f4c1ed1ba416c29f528207874c4e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3906fd079e81869a710c9835dc8884a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4b760ee7502c18027f67d95eb82210.png)
您最近一年使用:0次
2022-09-23更新
|
1524次组卷
|
5卷引用:江苏省丹阳高级中学、常州高级中学、南菁高级中学2022-2023学年高三上学期10月联考数学试题
江苏省丹阳高级中学、常州高级中学、南菁高级中学2022-2023学年高三上学期10月联考数学试题云南省大理市辖区2023届高三毕业生上学期区域性规模化统一检测数学试题(已下线)第03讲 直线、平面平行垂直的判定与性质(练)(已下线)考向28利用空间向量求空间角(重点)(已下线)第05讲 空间向量及其应用 (高频考点—精练)
名校
解题方法
3 . 如图所示,已知平行六面体
中,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/affbd9d7-14ff-4254-81d2-75d9184ec866.png?resizew=177)
(1)求
长度;
(2)求异面直线
与
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03305c49fc1e97c268296944e4e60f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/affbd9d7-14ff-4254-81d2-75d9184ec866.png?resizew=177)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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解题方法
4 . 如图,在棱长为2的正方体
中,线段DB的中点为F,点G在棱CD上,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/0f45fb62-574c-4848-bd0d-51ecbb547ab1.png?resizew=164)
(1)若E为棱
的中点,求证:
;
(2)求直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9e1ac9b20514f7fe9d2e00c37edede.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/0f45fb62-574c-4848-bd0d-51ecbb547ab1.png?resizew=164)
(1)若E为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fec5bd77cfc1313bc200480cc66c766.png)
您最近一年使用:0次
2023-01-04更新
|
253次组卷
|
2卷引用:皖豫名校联盟2022-2023学年高二上学期阶段性测试(二)数学试题
5 . 如图,在四棱锥
中,四边形
为矩形,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/2/38ae0c01-7683-49ad-9e13-5a8b91d2cf89.png?resizew=175)
(1)求线段
的长度;
(2)求异面直线
与
所成角的余弦值;
(3)若
为
的中点,证明:
.
![](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/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e598f65e3c3b3c1a047a575788baee94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/2/38ae0c01-7683-49ad-9e13-5a8b91d2cf89.png?resizew=175)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e253f0fbfa13dca5b4c7dce45fc47fe7.png)
您最近一年使用:0次
2023-01-01更新
|
573次组卷
|
4卷引用:安徽省滁州市定远县民族中学2022-2023学年高三上学期12月月考数学试题
安徽省滁州市定远县民族中学2022-2023学年高三上学期12月月考数学试题河南省郑州市第一〇二高级中学2023-2024学年高二上学期10月月考数学试题(已下线)模块一 专题11 空间向量与立体几何(已下线)第07讲 空间向量的数量积运算9种常见考法归类(1)
名校
解题方法
6 . 如图,在四棱锥
中,底面
为正方形,
底面
,
,E为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/f490ca37-7b90-4684-ad96-ca7b154023ae.png?resizew=137)
(1)求异面直线
与
所成角的大小;
(2)求平面
和平面
夹角的余弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a109c829d652632a88ade6924fcda206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/f490ca37-7b90-4684-ad96-ca7b154023ae.png?resizew=137)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2022-12-15更新
|
838次组卷
|
3卷引用:江西省临川第二中学2022-2023学年高二上学期第三次月考数学试题
名校
解题方法
7 . 如图,在棱长为1的正方体
中,E为线段
的中点,F为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/6c1f86c1-ca39-448d-80c6-dc0eaf4324ce.png?resizew=158)
(1)求直线
与直线
的所成角的余弦值;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/6c1f86c1-ca39-448d-80c6-dc0eaf4324ce.png?resizew=158)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1158eaa2e338f564eb18de5bef1d25.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
您最近一年使用:0次
2022-12-15更新
|
581次组卷
|
4卷引用:重庆市第七中学校2023-2024学年高二上学期第四次月考数学试题
名校
解题方法
8 . 如图,已知四棱锥
的底面
是直角梯形,
,
,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c707f0202ec1aa233e1eeacc7a4587d.png)
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c43fd5dd-9fcc-42f6-8593-bb91799d8b93.png?resizew=149)
(1)求
与
所成的角
(2)平面
与平面
所成的锐二面角余弦值
![](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/73d1c65a219c41f41ab34b9dd7a41bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c707f0202ec1aa233e1eeacc7a4587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/c43fd5dd-9fcc-42f6-8593-bb91799d8b93.png?resizew=149)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0cbbcc3d79bf999588882e7b1b4324.png)
您最近一年使用:0次
2022-12-14更新
|
459次组卷
|
4卷引用:江苏省淮安市涟水县第一中学2022-2023学年高三上学期第二次阶段检测数学试题
江苏省淮安市涟水县第一中学2022-2023学年高三上学期第二次阶段检测数学试题安徽省滁州市定远县育才学校2022-2023学年高二下学期开学考试数学试题(已下线)6.3.3 空间角的计算(练习)-2022-2023学年高二数学同步精品课堂(苏教版2019选择性必修第二册)江西省南昌县莲塘第一中学2022-2023学年高二上学期期末数学试题
名校
9 . 如图,直三棱柱ABC-A1B1C1中,M为BC的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/c74b04d7-99c5-488c-b277-c1bc070dc8a9.png?resizew=155)
(1)证明:A1B∥平面AMC1;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cfb38323095090b0fe5eee70b24210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffa995ac1b73394a4cecf085527f5e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/c74b04d7-99c5-488c-b277-c1bc070dc8a9.png?resizew=155)
(1)证明:A1B∥平面AMC1;
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
您最近一年使用:0次
2022-12-13更新
|
581次组卷
|
2卷引用:黑龙江省哈尔滨市第四中学校2022-2023学年高二上学期第一次月考数学试题
解题方法
10 . 已知空间四个点
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66af97892292102a6b723f39cdaf2f9.png)
(1)设
,求
与
夹角
的余弦值;
(2)求点D到平面ABC的距离d.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a2e98597f9e84b24bf0deaaf5541cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66af97892292102a6b723f39cdaf2f9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ba495e8f9fe02229a4248fdbfb4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)求点D到平面ABC的距离d.
您最近一年使用:0次