1 . 已知空间向量
,
,
.
(1)若
与
互相垂直,求实数
的值;
(2)若
,且
与
互相平行,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419830a9851022b7da1b6dc632d90e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9162f6b251803ff1c49fa8e878d0ad1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575e86e6694ee62509c73481f46b8204.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a06c8eae3652486cf9e416ce3a8ffc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496eeab5938122aa57a7fc521ef7c469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
2 . 已知向量
.
(1)求
;
(2)若向量
与
垂直,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac912dbe75df4d4207b5107942e4d1cd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb74499b8965b3f6c9acfbbb168df438.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
3 . 已知空间直角坐标系中四个点的坐标分别为:
.
(1)求
;
(2)若
,求x的值;
(3)若D点在平面ABC上,直接写出x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23fac84e323a1c6148d6222e106e3742.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a525625159560d77031e3329de541934.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2945cbc4ff0cb87a163b660d7b8d07fc.png)
(3)若D点在平面ABC上,直接写出x的值.
您最近一年使用:0次
2023-11-03更新
|
230次组卷
|
2卷引用:北京市人大附中2023-2024学年高二上学期期中数学试题
4 . 已知向量
,
,
.
(1)若
,求实数
的值;
(2)求
;
(3)若
,
,
不能构成空间向量的一个基底,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74eaff36755a7fc339de501c69365c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb48bdda5932311abf16f32339c4c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a28090124c5ed4e4762f5dde65c404.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1c5bcaa260128e281a12f6ef6aacbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3db87f99222f1705e122a6bd329c9f1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2023-11-02更新
|
337次组卷
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2卷引用:北京市丰台区2023-2024学年高二上学期期中练习数学试题(B)
5 . 如图,直三棱柱
中,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/5/0d64e6e9-e542-4bb5-9555-6577a80a103d.png?resizew=140)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/5/0d64e6e9-e542-4bb5-9555-6577a80a103d.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762b8cac66d86a013ba839266b023e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
2023-04-04更新
|
1774次组卷
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4卷引用:北京市海淀区2023届高三一模(期中)数学试题
名校
6 . 设
,向量
,
,
,且
,
.
(1)求
;
(2)求向量
与
夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be8cf8633d6b90276cffb3f5b962e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7078575f26f2976d86c243f3046286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd5edb35ede585f56b01203148a36e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4483c17746ee5603460beda6011743.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93af88a7628c71d642d3a6df067c15f5.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed492f7b29166ba5c1f0023b05a439c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb30a2fa155f2421850c0e7592b513d.png)
您最近一年使用:0次
2023-08-03更新
|
1451次组卷
|
16卷引用:北京理工大学附属中学2023-2024学年高二上学期期中练习数学试题
北京理工大学附属中学2023-2024学年高二上学期期中练习数学试题人教A版(2019) 选修第一册 数学奇书 第一章 学业评价(五)人教A版(2019) 选修第一册 数学奇书 第一章 空间向量与立体几何 1.3 空间向量及其运算的坐标表示 1.3.2 空间向量运算的坐标表示(已下线)高二上学期期中数学试卷(基础篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)1.3.2 空间向量运算的坐标表示练习山东省枣庄市第八中学2023-2024学年高二上学期开学摸底考试数学试题山东省德州市第一中学2023-2024学年高二上学期10月月考数学试题广东省阳江市两阳中学2023-2024学年高二上学期月考一数学试题广东省汕头市金山中学2023-2024学年高二上学期10月阶段考试数学试卷宁夏回族自治区银川市贺兰县第二高级中学2023-2024学年高二上学期10月第一次阶段性考试数学试题广东省东莞市四校2023-2024学年高二上学期期中联考数学试题(已下线)第1章 空间向量与立体几何单元测试基础卷-2023-2024学年高二上学期数学人教A版(2019)选择性必修第一册黑龙江省牡丹江市海林市朝鲜族中学2022-2023学年高二上学期第一次月考数学试题广东省梅州市五华县水寨中学学等五校2022-2023学年高二上学期10月联考数学试题广东省梅州市五校(虎山中学、丰顺中学、水寨中学、梅州中学、平远中学)2022-2023学年高二上学期期中联考数学试题(已下线)模块一 专题5《 空间向量运算》 A基础卷(苏教版)
解题方法
7 . 如图,在正方体
中,正方体的棱长为2,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/162d8817-3545-4032-8bc9-e3044449f5be.png?resizew=182)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值;
(3)求
到平面
的距离.
![](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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/162d8817-3545-4032-8bc9-e3044449f5be.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95acc4df88e4fd0d38cf4a64f16d2dc4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次
名校
8 . 已知向量
,
.
(1)若
,求
;
(2)求证:对任意
,
与
不垂直;
(3)若
与
轴平行,求
、
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45c7469ee6e876c4ffa4d87cd67d3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43e055e2aaa1b3d5200f5255b207d87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8e6a59ae1aa48966ba5ea0e205f7b6.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffa3e1ce447d158f6084a66841307a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67a5673958e175b00200a75e645c73c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0f5d6389672e98b7a226d86706c390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-11-02更新
|
236次组卷
|
2卷引用:北京市怀柔区第一中学2023-2024学年高二上学期10月月考数学试题
解题方法
9 . 如图:
平面
,四边形
为直角梯形,
,
,
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712178353414144/2712219612602368/STEM/f16df0e3-b571-4b4b-974b-249fb2098582.png?resizew=252)
(1)求证:平面
平面
;
(2)求二面角
的余弦值;
(3)在棱
上是否存在点Q,使得
平面
?若存在,求
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a483c1ffa8e2cf224eb0e20827287465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc1291b9c1bdcf6168ef4a91bde1566.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712178353414144/2712219612602368/STEM/f16df0e3-b571-4b4b-974b-249fb2098582.png?resizew=252)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36824d6beda179820ac115d1258e8a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45322cbfad26d6d4bd94c218478854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc953f0be1dafec1b4d1836cbafbf59.png)
您最近一年使用:0次
2021-05-02更新
|
1091次组卷
|
4卷引用:北京卷专题20空间向量与立体几何(解答题)
北京卷专题20空间向量与立体几何(解答题)北京市门头沟区2021届高三二模数学试题(已下线)专题02 立体几何中存在性问题的向量解法-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)(已下线)专题3.6 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)