名校
1 . 已知空间向量
,
,若
,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5143c22699432c66143b1d70cafcb57a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa83017d54612e65f5cb0833ce8fc01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1afa49dbaa99a0d7a7a6d18b3fe42091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
A.0 | B.2 | C.![]() | D.![]() |
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名校
解题方法
2 . 如图所示棱长为1的正四面体
,
、
分别为
、
中点,
为靠近
的三等分点.记
,
.
,
,求
的最小值;
(2)求证:
平面
.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d458bed4c0f3e91667eb8705c9c90d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/415c6484536cc61efd5529fcb0b15eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037d31ba398cccf9770084cfdedaf045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9007ec6447a9428dadb4fdb7ae9bae.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dc8826770249f3996b8a188c03da92.png)
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2024-05-03更新
|
307次组卷
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3卷引用:湖北省荆州市荆州中学2023-2024学年高一下学期5月月考数学试卷
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3 . 在三棱柱
中,
是
的中点,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8bd24324d1a117e642beee2ee27545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da6f8b83986e9011727c96c3daf4307.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 已知
(a,
)是直线l的方向向量,
是平面
的法向量,如果
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfc3b155435130b8c1d0e66484a4727.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8752ee706196b497099ddd8342ef3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3849dacb9cd91d905551d858ffdd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c656aab9776eff87154d726241066459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfc3b155435130b8c1d0e66484a4727.png)
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5 . 空间四边形
中,
,
,
,点
为
中点,点
为
靠近
的三等分点,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381985fdee6a1ac3ad4a73f5f653b84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad299e2782c072d27e1c54422cc8fc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-03-06更新
|
453次组卷
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3卷引用:湖北省云学名校联盟2023-2024学年高二下学期3月联考数学试卷
6 . 已知向量
,向量
在向量
上的投影向量为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0950549c5bfe6479af02460efab1fc18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-04更新
|
989次组卷
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8卷引用:湖北省鄂西南三校2023-2024学年高二下学期三月联考数学试卷
湖北省鄂西南三校2023-2024学年高二下学期三月联考数学试卷山东省烟台第一中学2023-2024学年高二下学期2月月考数学试题江苏省南通市海门中学2023-2024学年高二下学期3月阶段练习数学试卷河南省周口市西华县第三高级中学2023-2024学年高二下学期第一次月考数学试题-(已下线)模块3 第3套 复盘卷福建省莆田第五中学2023-2024学年高二下学期第一次月考数学试卷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01 空间向量表示及运算--高二期末考点大串讲(苏教版2019选择性必修第二册)
7 . 在四面体
中,M点在线段
上,且
,G是
的重心,已知
,
,
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe72d1b634f1e89d8699e605e7d46af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420ad6159fc091d6a5ffddf0676d2662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c2e7e9fd8519fd1c293cc577408263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40f8ef7e3af00c41f85a20578afdb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53a4722fb7b67eeb4145b491c456ff.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-28更新
|
229次组卷
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3卷引用:湖北省荆门市2023-2024学年高二上学期1月期末学业水平检测数学试题
湖北省荆门市2023-2024学年高二上学期1月期末学业水平检测数学试题江苏省常州市联盟学校2023-2024学年高二下学期3月阶段调研数学试题(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】
名校
解题方法
8 . 已知
,
,其中
,
,若
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b93656d46e8bd1ac7e9d14659d42c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c5d62184910f1faa373f8971f8b240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd93ee03569849295ebde055410d1b84.png)
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9 . 如图,四棱锥
中,
为等腰直角三角形,四边形
为菱形,
,
,E,F分别为CD,PD的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/ffd3d4c6-eb41-4062-b7d8-e3ef22793ba1.png?resizew=149)
(1)求证:
;
(2)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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14f698605a196cf83ccba6a601d0e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/ffd3d4c6-eb41-4062-b7d8-e3ef22793ba1.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00e0cff0876c4183a47f1272cf9928.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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10 . 对于任意向量
定义运算:
.若向量
,向量
为单位向量,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf9fc45e6dc0579eda8f3f0d63a09c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb27737e8a85ed60579509b5ff53a32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db35dbee504e3e66bfd03c24e4b7322.png)
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