名校
1 . 已知向量
,
.
(1)求
;
(2)求
;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e459c85baeaafc79427efdb9d3c8bf3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ab30ac1ff177d77f9961ab6af4e562.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb6118172f384a565afcdfd84e9cdb0.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7735616d46e9925e7ce1a9f58be33a5f.png)
您最近一年使用:0次
名校
2 . 已知空间向量
.
(1)计算
和
;
(2)求
与
夹角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3d8e2a1761d761e257ebf8d63df38a.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f0484158c0bb8ef08faf224bba82e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0378850babaf830f1ac2f580c84d43.png)
(2)求
![](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)
您最近一年使用:0次
2024-02-24更新
|
282次组卷
|
2卷引用:浙江省杭州外国语学校2023-2024学年高一下学期期中考试数学试卷
3 . 已知空间向量
.
(1)若
,求实数
与
的值;
(2)若
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cbd199230f153bfe138edd14735684.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe3159fede573644c8cf10c763fd82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0404f82aa062c72a4f6fcbfe9f4db167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cba22ec376fbe8aa2f079a1c6daa790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cfe95f520c7b454ceabb2ae9af0a87.png)
您最近一年使用:0次
4 . 已知向量
与向量
共线,且
,
,
(1)求向量
的坐标;
(2)求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78f8f5954e131eb1f3c151653f70312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793be84d1bf071f4c80cf98adb398e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989e734596b056b23ecbfd945019c496.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
5 . 已知空间四点
,
,
和
,求证:四边形
是梯形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356585c75a5db4754720dcab6a58fb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dc6169910db42dbbd215fadbe90ff67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ddc9c616b1912bfdfc52e564bf5354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164d7860e4b8e67e07fb1e189f984b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-10-05更新
|
274次组卷
|
6卷引用:6.3.4平面向量数乘运算的坐标表示练习
6.3.4平面向量数乘运算的坐标表示练习(已下线)6.3.2+6.3.3+6.3.4平面向量的正交分解及坐标表示【第三课】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)专题1.4 平面向量基本定理及坐标表示-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)模块一 专题2 平面向量基本定理与坐标运算(讲)(已下线)模块一 专题4 平面向量基本定理与坐标运算(讲)北师大版高一期中湘教版(2019)选择性必修第二册课本例题2.3.2空间向量运算的坐标表示
名校
6 . 已知空间中三点
,
,
,设
,
.
(1)若向量
与
互相垂直,求k的值;
(2)若
,且
,求向量
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5e428213f946350934bc876fba5514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9eaf8136d289e745dd56ec4642aa7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642abd464232937a2d8e6ebc70273f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d458bed4c0f3e91667eb8705c9c90d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/415c6484536cc61efd5529fcb0b15eb9.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9441846da0868582298cece138bec3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1fa7538549bf04c02a09ead1745ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78aefee3211ca8d99b9af016e87617ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
您最近一年使用:0次
2023-09-27更新
|
100次组卷
|
2卷引用:陕西省延安市延川县中学2023-2024学年高一上学期第一次月考数学试题
7 . 已知点
,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde14ad18e9b6f0422576be3ee98d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe51a2c12e6f14dea578d8adf9f81fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c668a025c66a4ee803f6e07258a4c049.png)
您最近一年使用:0次
8 . 已知向量
,求:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde969007c65b2b6304ef0d53bc629d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b5bbe37cc6de8ceb50091f49ce8ef3.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1669d094b7eaa23544db2e3b85d766a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa707c74a63baeb2e72e3fd0bc2e884f.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beaefc47c401809b42f5e980f880dd9d.png)
您最近一年使用:0次
2023-09-17更新
|
257次组卷
|
2卷引用:人教B版(2019)选择性必修第一册课本习题第一章本章小结
9 . 如图,在棱长为
的正方体
中,
是
的中点,
是
的中点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963746756329472/2973384084193280/STEM/eebe3ac4-5602-46c6-8643-2e581f11fd17.png?resizew=144)
(1)试建立适当的坐标系,并确定
、
、
三点的坐标;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963746756329472/2973384084193280/STEM/eebe3ac4-5602-46c6-8643-2e581f11fd17.png?resizew=144)
(1)试建立适当的坐标系,并确定
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f2a1b0fab623ed692528b08c8156db.png)
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解题方法
10 . 在棱长为1的正方体
中,E为
的中点,P、Q是正方体表面上相异两点.若P、Q均在平面
上,满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/99c9b07e-6aa8-45f0-a4f0-4b696262814c.png?resizew=154)
(1)判断PQ与BD的位置关系;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c767875a64fea20109b86411e00237a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2920626a0513c469e1f08ea59f6b37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/99c9b07e-6aa8-45f0-a4f0-4b696262814c.png?resizew=154)
(1)判断PQ与BD的位置关系;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70a36c81024b207988f8540498c5c7c.png)
您最近一年使用:0次
2022-05-05更新
|
192次组卷
|
3卷引用:第07讲 空间向量的应用 (1)