名校
解题方法
1 . 已知
,若
,则实数
=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08024bba861d3ea48ff8254d905f0d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead4767424866f1453c464a93b3ca8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.﹣4 | B.1 | C.2 | D.6 |
您最近一年使用:0次
2024-06-07更新
|
429次组卷
|
2卷引用:广东省广州科学城中学2023-2024学年高一下学期期中检测数学试题
名校
2 . 已知向量
,
,则向量
在向量
方向上的投影向量为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55fcd6e54fa0ff9436cc514945d4a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0f1cdcb43a0d77cc9231cfa2909e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
3 . 已知向量
是同一平面内的三个向量,其中
.
(1)若
,且
,求向量
的坐标;
(2)若
是单位向量,且
,求
与
的夹角
.
(3)若
,求向量
在向量
上的投影向量(用坐标表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d171c0b75d097413232a4a5332d03e1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889311e281d855090dd1096f920c4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd43c3c9a578b91fe832c4c2477103c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb9e6b6ec47e6649b945db2a6d7ad72.png)
![](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/c24095e409b025db711f14be783a406c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f590b40f1781cb17df6d99920064b15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b76118bdca6c463cfb19b66f30281c4.png)
您最近一年使用:0次
2024-06-03更新
|
504次组卷
|
2卷引用:广东省广州市第六十五中学2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
4 . 已知向量
,若B,C,D三点共线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5071620a9137ef5060b7b22a4c2fb739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
您最近一年使用:0次
2024-05-20更新
|
569次组卷
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2卷引用:广东省广州市白云艺术中学2023-2024学年高一下学期期中数学试题
名校
5 . 已知
分别是
的边
的中点,且
,有下列四个等式:①
;②
;③
;④
.其中正确的等式的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5b88ec996d2d117987e7303cefe4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b372e638a9dbed3bbf92454d816d212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b214e4b9d745344a18bd684c5ce917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbdf926234d61a3c26f8c42cbb28441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6af651faa7b81ce7b4b9c0916f3c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2315bceb4956009ac21516cf36e0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9fbf69745aa70c5172303ec5374289.png)
A.①③ | B.①②④ | C.②③ | D.②③④ |
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6 . 已知:向量
.
(1)求
;
(2)求
夹角的余弦值;
(3)若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef8e420725b4ee2fb9db0cab07d4ec6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d6f122739bfe3e5182375b585870a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb87bef0e638511ec0f86a176baea7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7 . 在平行四边形
中,
为
的中点,
,
与
交于点
,若
,
,则
( )
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c21a8c8f5987d350cbab0d56d9bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8a8c17891ffbda9b616bee26d67e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e503b5f39429c162a82f047195e294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df40e9eabd3898c8232aa070d243fb0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
8 . 如图,在
的边上做匀速运动的点
,当
时分别从点
,
,
出发,各以定速度向点
前进,当
时分别到达点
.
,点
为三角形
的重心,试用向量
线性表示
(注:三角形的重心为三角形三边中线的公共点)
(2)若
的面积为
,求
的面积的最小值.
(3)试探求在运动过程中,
的重心如何变化?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba399f21f2a4f9b94066ea578865a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba399f21f2a4f9b94066ea578865a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ba495e8f9fe02229a4248fdbfb4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2caf2e65bebc1523f8e89b59a90f2ab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
(3)试探求在运动过程中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
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解题方法
9 . 已知
和
是两个不共线的向量,
,
,且
与
是共线向量,则实数
的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a724b7e1ff94bc42112bd470fb4441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d5a9b6e288f1eebd65be8abe98b291.png)
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
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10 . 如图所示,在
中,点O是BC的中点,过点O的直线分别交直线AB、AC于不同的两点M、N,若
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328e8ec9120d4f382d63802421770a14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a10a8252aaca38bed5ab3657e4c122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd93ee03569849295ebde055410d1b84.png)
A.5 | B.9 | C.![]() | D.![]() |
您最近一年使用:0次
2024-05-04更新
|
724次组卷
|
5卷引用:广东省广州市第八十九中学2023-2024学年高一下学期期中考试数学试卷