1 . 如图所示,在平行四边形
中,
为
的中点,
为
靠近
的三等分点,求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7208dc83c7802ac8587b1d41daa28a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89b83073eb132190d43a4b49733038c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/f65bf75c-7430-430f-bd9d-8bb464049b71.png?resizew=174)
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2019-10-09更新
|
1288次组卷
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2卷引用:人教A版 必杀技 第二章 平面向量 2.3.1平面向量基本定理
名校
2 . 已知两个非零向量
不共线,
.
(1)证明:
三点共线;
(2)试确定实数
,使
与
共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d184ae171c511d3ab7eebb7dbb4eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f773b5ebfaf2c5c6624a323f7e4a99.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1378530dfec264f4bf99a179826dc957.png)
(2)试确定实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea1f268299d57e5362182760a5961af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f200069e313c5863a4efab246fd347a.png)
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2019-10-09更新
|
949次组卷
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3卷引用:人教A版 必杀技 第二章 平面向量 第2.2节综合训练
3 . 已知两个非零向量
不共线,如果
,
(1)求证:A,B,D三点共线;
(2)若
,且
,求向量
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42503437fb44722722cd20835f11d233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f04fb07cd3e9460ff21e1bee9ed995.png)
(1)求证:A,B,D三点共线;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94ec50c2dca920075714497200a1f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5d7137a6af77d87717a7d73b06decd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42503437fb44722722cd20835f11d233.png)
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2019-06-17更新
|
934次组卷
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2卷引用:【校级联考】浙江省2018-2019学年第二学期杭州八联盟期中联考高一年级数学学科试题
名校
4 .
已知A、B、P三点共线,O为任意一点,若
求证
;
如图所示,已知
中,点B关于点A的对称点为C,D在线段OB上,且
,DC和OA相交于点
设
,
.若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6226cc8306a652f9eac1f4c2f6e6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a816a6fed5c4bdbeebb19bd21ee247b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66346fb74f131b217e668d44939e5c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aca8e59d29771ec2c5a053ed35e438e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cba734c5d000acc2161529a539123b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2576165f1246c356e26823a48cfc4667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25e4f91ee364ac0b1490533028cbfb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db1e87964e63f0df4146ed0fe4d1d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b109838e10fd78330c54d0f03887549.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/7724c2d5-76fa-44ab-994d-fe2c20f8a789.png?resizew=142)
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名校
5 . 已知两个非零向量
.
(Ⅰ)若向量
是夹角为120°的单位向量,试确定实数
,使
和
垂直;
(Ⅱ)若
,
,
,求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bb5c33537724ed700a9b93ed3078ce.png)
(Ⅰ)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bb5c33537724ed700a9b93ed3078ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2bc7ffe59b30bbacaf43dab9744df05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8deec23d86552cfa730788a30a55ea0.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec021bdc7cf90fadb60bbebd82d5c0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610fcb9932be60fbfb4aa6b8f00c355a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f130742e3e2390377c2527066c1efefa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ff675af39ec7beae91410e4297120c.png)
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2018-09-13更新
|
348次组卷
|
6卷引用:【全国校级联考】福建省龙岩市非一级达标校2017~2018学年第二学期期末高一教学质量检查数学试题
名校
6 . 在平面直角坐标系中,O为坐标原点,A、B、C三点满足
.
求证:A、B、C三点共线;
已知
、
,
,
的最小值为5,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431d15b80cc65e037b35bc10bd8d45e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6611c73064bda197766c00b448dd0030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f8c513fdf6f75cdd4f441e35ecfc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a848eab8a7cd5094a8dc37f9b91f38b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a39a25091e39b138526e12a3937872.png)
您最近一年使用:0次
2018-03-02更新
|
1941次组卷
|
9卷引用:北京101中学2017-2018学年高一上学期期末考试数学试题
名校
7 . 设
不共线,且
.
(1)若
,求证:
三点共线;
(2)若
三点共线,问:
是否为定值?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870621330877caa08df79df91fc4ff4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1ba5acc2c716d8a3d36de3b6a3ca87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c0ec201ece369cea29b016bdfe50bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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2018-01-06更新
|
837次组卷
|
5卷引用:江苏省南通市海安高级中学2016-2017学年高一下学期期末考试数学试题
江苏省南通市海安高级中学2016-2017学年高一下学期期末考试数学试题(已下线)2017-2018学年第一学期期末复习备考之精准复习模拟题高一江苏版数学试题(A卷)人教B版(2019) 必修第二册 过关斩将 第六章 6.2.1 向量基本定理沪教版(2020) 必修第二册 同步跟踪练习 第8章 平面向量 8.3.1平面向量的分解定理沪教版(2020) 必修第二册 同步跟踪练习 第8章 8.3.1 向量基本定理
名校
8 . 在平面直角坐标系中,
为坐标原点,
三点满足
.
(1)求证:
三点共线;
(2)已知
,
的最小值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7453d507d0c0c7c10d5f73dca6dceb5d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311995bf3e561f255d947b8a75ca0d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f18c358e515979c5eea9a6617ebc151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2018-04-25更新
|
791次组卷
|
7卷引用:2014-2015学年浙江省台州市书生中学高一下学期起始考数学试卷
9 . 已知向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e524c2988704ecc0d41cc9607b4c1c64.png)
(1)若
,求证:
;
(2)若向量
共线,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e524c2988704ecc0d41cc9607b4c1c64.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6778e27ec765abb44b3eeb0f80e20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb58883caf5c8ca1e94389839d294b6.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64fa2fcefaf3d8868da0cb52877c5247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e225297418ba60d303578d96116f2e22.png)
您最近一年使用:0次
2018-02-27更新
|
785次组卷
|
4卷引用:江苏省扬州市2017~2018学年度高一第一学期期末调研测试数学试题
江苏省扬州市2017~2018学年度高一第一学期期末调研测试数学试题(已下线)6.3.2 平面向量数量积的坐标表示(精讲)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)福建省南平市2022-2023学年高一下学期期末数学冲刺卷试题(三)安徽省滁州市新锐学校2019-2020学年高二上学期期末数学试题
10 . 如图,平行四边形ABCD中,点M在AB的延长线上,且BM=
AB,点N在BC上,且BN=
BC.求证:M、N、D三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://img.xkw.com/dksih/QBM/2018/2/21/1887073718788096/1890074568851456/STEM/eb1b66842beb4bdb8e9ab4704e4b0fb2.png?resizew=172)
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