如图,在四面体OABC中,M是棱OA上靠近A的三等分点,N是棱BC的中点,P是线段MN的中点.设
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/2/12/2915051778998272/2918205736140800/STEM/900fd4bb-2233-40b0-8ad4-c49e36e6f946.png?resizew=166)
(1)用
,
,
表示向量
;
(2)若
,且满足 (从下列三个条件中任选一个,填上序号:①
;②
;③
,则可求出
的值;并求出
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ac5f94e56c4679a32df00c5bb57964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63666d7cc3b50ada407f904098e163c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77e78c91e893f7759482b8de993020f.png)
![](https://img.xkw.com/dksih/QBM/2022/2/12/2915051778998272/2918205736140800/STEM/900fd4bb-2233-40b0-8ad4-c49e36e6f946.png?resizew=166)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524594bf0942ed86f56fc1eee120a81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd35cc30ce0d3a5ca2bbeec79a9ce1ee.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c6ce8d4f309cc186f0a5a1739b35d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b288fac1920a864af933fbd7beede14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf545b8ec5c569ecfa2df848bf56372b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f211c92e0c22f3ed26da4cf9109f99fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36216e68d3e793e93f82bb3fd2bdcec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36216e68d3e793e93f82bb3fd2bdcec6.png)
21-22高二下·浙江杭州·开学考试 查看更多[7]
浙江省杭州市2021-2022学年高二下学期开学测试数学试题江苏省扬州中学2021-2022学年高二下学期3月月考数学试题(已下线)专题1.3 空间向量及其运算的坐标表示(6类必考点)安徽省宿州市萧县鹏程中学2021-2022学年高一远志班下学期第一次质量检测数学试题(已下线)6.2.1空间向量基本定理(2)(已下线)1.2 空间向量基本定理【第三练】(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3 空间向量基底法(三)【基础版】
更新时间:2022-02-17 09:27:40
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【推荐1】如图,棱长为
的正四面体(四个面都是正三角形)
,
是棱
的中点,点
在线段
上,点
在线段
上,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/09b147fe-ed07-4852-89df-e1a29c45165f.png?resizew=197)
(1)用向量
,
,
表示
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ac9904467780bca2f8d563d1ac7f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8de8d51bd35d920e70be7364b4915d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/09b147fe-ed07-4852-89df-e1a29c45165f.png?resizew=197)
(1)用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ec3efaa6b6ff5769e8999df5714a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f0e6d3115e900f1a359ec4f894e8896.png)
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【推荐2】已知
.
(1)求
在
上的投影向量;
(2)若四边形
是平行四边形,求顶点D的坐标;
(3)若点
,求点P到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3608d74323e208b980076027386fdd0c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6586e95e1095f1159d82b927781e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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【推荐1】如图,在三棱柱
中,
,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/d6588c04-31f1-435d-9203-3fba3259b98b.png?resizew=149)
(1)试用向量
表示
,并求
.
(2)在平行四边形
内是否存在一点
,使得
平面
?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/7ead002fb15a14420603e39228c23615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182caf131fe710c71695f83030c734c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/d6588c04-31f1-435d-9203-3fba3259b98b.png?resizew=149)
(1)试用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a027f6aae91db1a4e7403c13a7d930d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855ab25eed88772c2166fe14c3971013.png)
(2)在平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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【推荐2】如图,三棱柱
中,M为AB上靠近于A的三等分点,N为
中点,记
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/11/10/2848359063805952/2850594040627200/STEM/cf2c8955b96e4700af3c3a1d9786c26a.png?resizew=237)
(1)试用
表示
.
(2)若三棱柱
各棱长均为6,且
,求直线MN与AB所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b536ac375a0b74e9c7efbc585f987f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0c566d351afa62188696128ce18f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc6f461f4715a6c25e8df41ab35a565.png)
![](https://img.xkw.com/dksih/QBM/2021/11/10/2848359063805952/2850594040627200/STEM/cf2c8955b96e4700af3c3a1d9786c26a.png?resizew=237)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7cad34fccd0fe584087604e863f352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb93bee3008094ff1faf0dc99eba9318.png)
(2)若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5fd85ee3df1c1c7c499c9f500c99c4.png)
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