1 . 如图所示,平行六面体
中,
,
.
(1)用向量
表示向量
,并求
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d20d9a8058985d9847ddd99046fdb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a27ea00fee0b2571c6f1e8cc943a1d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/ed55734c-a610-409b-8b20-2f769dfb319c.png?resizew=113)
(1)用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68873c59a21b0cd408cdf2b47d51096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccec46f7c4da972fef6e940158628242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33e3af60b6aa94f39bbd04470d2e404.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388e976ab53ad76d39c74b59a09b1663.png)
您最近一年使用:0次
2 . 如图E,F分别是长方体
的棱AB,CD的中点,化简下列表达式:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/51a0554b-3a4d-46f3-b567-adc5b1a92354.png?resizew=196)
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/22/51a0554b-3a4d-46f3-b567-adc5b1a92354.png?resizew=196)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8bff9897ed3b72ee1fdbe43ec93f0dd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b62e7149eba7c5306cd4b0fa59c91d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bc880720c71266c8a705c23405bff9.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db454f0bc155736ecc94f0efd1bd09e.png)
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名校
解题方法
3 . 如图,在直三棱柱
中,
,
分别为
,
的中点.
,求
的值;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c45fb1bd3936fe41d53ea3ac772bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d86dcb456ab7ae39a37c70b372848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2023-12-24更新
|
772次组卷
|
7卷引用:贵州省六盘水市水城区2023-2024学年高二上学期12月质量监测数学试题
贵州省六盘水市水城区2023-2024学年高二上学期12月质量监测数学试题河北省邢台市质检联盟2023-2024学年高二上学期第四次月考(12月)数学试题广东省东莞市东华高级中学2024届高三一模数学试题吉林省部分名校2023-2024学年高二上学期期末联合考试数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(六)新疆兵团地州学校2023-2024学年高二上学期期末联考数学试题(已下线)高二数学开学摸底考 01(人教B版2019选择性必修第一册+第二册)-2023-2024学年高二数学下学期开学摸底考试卷
名校
4 . 如图,在棱长为4的正四面体
中,
是
的中点,
,记
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/a7bd56e6-78be-42bd-8d4e-5f7d6a01d14f.png?resizew=187)
(1)求
的值;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057505ce7b11cfb85e490cc44e88ccc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e306327dbe115902d2fe451395b48b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/a7bd56e6-78be-42bd-8d4e-5f7d6a01d14f.png?resizew=187)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41d51041342c5ffbb4359a3ac33342d.png)
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2023-12-19更新
|
290次组卷
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6卷引用:贵州省2023-2024学年高二上学期12月月考数学试题
解题方法
5 . 如图,三棱锥中,点D、E分别为
和
的中点,设
,
,
.
(1)试用
![](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/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eae81e4e5598e38529d8b0fca218e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
您最近一年使用:0次
名校
6 . 如图,平行六面体
的底面是菱形,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef3d3128ce3f5799c39dd6b8290122e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/d4011eb3-e96d-4922-b168-9d7faf9d4842.png?resizew=167)
(1)用空间的一个基底
表示
,并求
的长;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef3d3128ce3f5799c39dd6b8290122e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/1/d4011eb3-e96d-4922-b168-9d7faf9d4842.png?resizew=167)
(1)用空间的一个基底
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed66bde4aaae35dc7a1ccc292a6ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
您最近一年使用:0次
2023-11-29更新
|
132次组卷
|
2卷引用:四川省成都市郫都区2023-2024学年高二上学期期中数学试题
解题方法
7 . 如图,在空间四边形
中,
,点
为
的中点,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/4af2875a-e856-456a-9066-3b33d6f98fcb.png?resizew=169)
(1)试用向量
表示向量
;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c81ddf20b4da9a674722376b84910e.png)
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dc95aa3f1f159dbf4c61239a8df7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc5343d0ed7b449971c7ba787a621fa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/4af2875a-e856-456a-9066-3b33d6f98fcb.png?resizew=169)
(1)试用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21909dd065ccc349a2cbfd4c3cf4976b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c81ddf20b4da9a674722376b84910e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432aca761e9fa97d3728a8038de81e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68cb701aa80a3335db37a5eb420fcb64.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,已知平行六面体
中,底面ABCD是边长为1的正方形,
,
.
的长度;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0aa7d7faf508bacfd7fa5ae00affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce64c7cf095a20894e9ddd0d95992a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
您最近一年使用:0次
2023-11-27更新
|
185次组卷
|
3卷引用:四川省凉山州西昌市2023-2024学年高二上学期期中检测数学试题
四川省凉山州西昌市2023-2024学年高二上学期期中检测数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点4 空间向量基底法(四)【基础版】甘肃省天水市第一中学2023-2024学年高二下学期4月学段检测数学试题
9 . 已知空间四边形
中,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5f7fd37cdb01d649bd074bc79d7339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9acdabbbcfa6185a39659a416a4218.png)
您最近一年使用:0次
10 . 如图,在三棱柱
中,
分别为
和
的中点,设
.
(1)用
表示向量
;
(2)若
,
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb5f474b6067ce50ca48790c45fd587.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/e1aec47f-0dba-4964-a4ee-64f4bd3ec162.png?resizew=162)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8c53645db602c72b00b599c2c0ff97.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9523d53df3a91e8bc9abaee19a1fb753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981978eee3927889e8527272c98468b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9eac7e04c7e650dfbf10ea05ea6045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5a8d419738d657c20fa8d1ba91c053.png)
您最近一年使用:0次
2023-11-15更新
|
391次组卷
|
5卷引用:贵州省2023-2024学年高二上学期11月期中联考数学试题
贵州省2023-2024学年高二上学期11月期中联考数学试题辽宁省抚顺市六校2023-2024学年高二上学期期中考试数学试题陕西省汉中市多校联考2023-2024学年高二上学期12月月考数学试题(已下线)专题01 空间向量及其应用常考题型归纳(1)(已下线)6.1 空间向量及其运算(5)