名校
1 . 在平面上,给定非零向量
,对任意向量
,定义
.
(1)若
=(-1,3),
=(2,3),求
;
(2)若
=(2,1),位置向量
的终点在直线x+y+1=0上,求位置向量
终点轨迹方程;
(3)对任意两个向量
,求证∶
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9181079d14f7c1bc9b5b2624f94edca.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(3)对任意两个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1721476f7850842ba3dc3d8be33c3723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835ebae7895448fd3d6551b953565ab3.png)
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20-21高一·江苏·课后作业
2 . 设P,Q分别是梯形ABCD的对角线AC与BD的中点
![](https://img.xkw.com/dksih/QBM/2021/3/9/2674036069908480/2674215109885952/STEM/f68c0783e6af42918ecca03259c6d218.png?resizew=260)
(1)试用向量证明:PQ
AB;
(2)若AB=3CD,求PQ:AB的值.
![](https://img.xkw.com/dksih/QBM/2021/3/9/2674036069908480/2674215109885952/STEM/f68c0783e6af42918ecca03259c6d218.png?resizew=260)
(1)试用向量证明:PQ
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
(2)若AB=3CD,求PQ:AB的值.
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2021-03-09更新
|
836次组卷
|
7卷引用:9.2.2 向量的数乘 2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)
(已下线)9.2.2 向量的数乘 2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)(已下线)6.3平面向量线性运算的应用-2021-2022学年高一数学同步知识梳理+考点精讲精练(人教B版2019必修第二册)(已下线)第05讲 平面向量-【寒假自学课】2022年高一数学寒假精品课(苏教版2019必修第二册)(已下线)6.4.1 平面几何中的向量方法(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)(已下线)专题07 向量的应用-【寒假自学课】(苏教版2019)(已下线)专题6.5 平面向量的应用-举一反三系列(已下线)6.4.1 平面几何中的向量方法-同步题型分类归纳讲与练(人教A版2019必修第二册)
3 . (1)设
,
是两个不共线的向量,
,
,
,证明:A,B,D三点共线.
(2)已知E,F分别是
边AB,AC上的点,且
,
.如果
,
,试用向量
,
表示
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc016d5ddad0b2c04e537d0980cb5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48498c5a8f41f2acbdfb391324b6e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810932e26f259fb34e88a64fa1861465.png)
(2)已知E,F分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b12aa9d4f934868c3e4f51f73e7c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aee316a7843afbe76506612f597bf71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291b593c5c12e80f6d66adddb24eb99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dbdda9fb5813e20558da8aeeee4b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d792a2aa25763e14cc2863be3887000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88369a480ff098461307038ceb224e2.png)
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4 . 已知圆O的方程为
,圆O与y轴的交点为A,B(点A在点B的上方),直线
与圆O相交于M,N两点
(1)当k=1时,求弦长
;
(2)若直线y=4与直线BM交于点D,求证:D、A、N三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
(1)当k=1时,求弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
(2)若直线y=4与直线BM交于点D,求证:D、A、N三点共线.
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名校
解题方法
5 . 在平面直角坐标系中,O为坐标原点,C,P,Q三点满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b505e5775d206e19c1dd5117a6be2e89.png)
(1)求证:C,P,Q三点共线;
(2)若
,
(
),则
(
)的最小值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b505e5775d206e19c1dd5117a6be2e89.png)
(1)求证:C,P,Q三点共线;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e523f0fd6c95477c3fb3021db59711ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbcc972c140f754f7ae93284991eacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a14f8dddd68c90a12a30a71b01f654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
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6 . 如图,已知两条抛物线
和
,过原点O的两条直线
和
,
与
分别交于
两点,
与
分别交于
两点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1312cef5566f80612face7ebc1df5cbc.png)
(2)过原点
作直线
(异于
,
)与
分别交于
两点.记
与
的面积分别为
与
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e39bd21af422662049290a3aa4841b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0683b56d0a6fb3a5b2c2b0d3f264b5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1312cef5566f80612face7ebc1df5cbc.png)
(2)过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828dc8dc7259c510b6d63abf40f60e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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7 . 如图所示,已知D,E分别为
的边
,
的中点,延长
至点M使
,延长
至点N使
,求证:M,A,N三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d146265934394d0cca5eea052bf651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b748fe903d4842a61319d860e05edf30.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e108cd41-ae02-4e11-b94c-e849f338db7a.png?resizew=196)
您最近一年使用:0次
2020-02-02更新
|
403次组卷
|
3卷引用:人教A版(2019) 必修第二册 逆袭之路 第六章 6.2.3 向量的数乘运算
人教A版(2019) 必修第二册 逆袭之路 第六章 6.2.3 向量的数乘运算人教B版(2019) 必修第二册 逆袭之路 第六章 6.1 平面向量及其线性运算 6.1.5 向量的线性运算(已下线)6.2.1 平面向量的线性运算(精练)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)
解题方法
8 . 已知
,
是两个不共线的向量,若
,
,
,求证:A,B,D三点共线;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b04618e5b2db68f2de6ba68972c505c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842cc71f3a2640e8ce485d8d6f2bf03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a4d74f8db967a4e0c2b157bb93cd6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c0743f436d4e109fa19b10793a8308.png)
您最近一年使用:0次
2020-04-07更新
|
610次组卷
|
4卷引用:人教A版(2019) 必修第二册 逆袭之路 第六章 6.2.3 向量的数乘运算
人教A版(2019) 必修第二册 逆袭之路 第六章 6.2.3 向量的数乘运算专题02 向量的数乘运算、数量积(知识精讲)-【新教材精创】2019-2020高一数学新教材知识讲学(人教A版必修第二册)-《高中新教材知识讲学》(已下线)6.2.1 平面向量的线性运算(精练)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)陕西省西安市2022-2023学年高一下学期第一次月考数学模拟试题
名校
9 . 已知
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4019bb5be0b93c547278632a316b5099.png)
,若
,
,
.
(1)证明:
为等边三角形;
(2)若
的面积为
,求
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4019bb5be0b93c547278632a316b5099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8b50bf37cfd8cecf855ea7a817b0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75b0c90bf6ac26c6b94bf2b3d2ebc68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61348e4bd81707e2e3f6f18303276c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fe866afef386a8c316ccdb35ed54dd.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c7b80a27c9905561daaf816b05ae75.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4123975f257306440158659634c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d73b2448f9aba5ca9885fd1edd1bca1.png)
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2020-03-19更新
|
328次组卷
|
3卷引用:2020届贵州省贵阳市第三十八中学高三上学期模拟理科数学试题
解题方法
10 . 如图所示,在平行四边形
中,
,
,M为
的中点,点N在
上,且
.证明:M,N,C三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46927389fcb9c1ab2d8fb4bc1e60793a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11fed0e4135ea42366959e4e305bd7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d562c896d69cfa13be4ad8d5f3a731.png)
![](https://img.xkw.com/dksih/QBM/2020/2/11/2396765285163008/2396823335010304/STEM/6ffab142693e4a5f9830c0ee4c8d271b.png?resizew=245)
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