20-21高一下·上海浦东新·阶段练习
名校
解题方法
1 . (1)请你利用数量积的定义(非坐标运算公式)证明:
;
(2)已知向量
与
的夹角为
,
,
,记
,
,若
,求实数k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4251b01d3a622638a54f4b839bacf95.png)
(2)已知向量
![](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/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f18996bd00253c3ad9f91780103affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03ef3e7fb905b47f36c4630fcc65dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05dbf33b2c0984ee458fa9dc91ecf412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495af06bb4bfd6573b9a0ed151d03af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ee59964f020fc52b5ba66a3f5fcc3c.png)
您最近一年使用:0次
名校
2 . 已知O为直角坐标系原点,
,
,
与
垂直,
与
平行.
(1)求向量
在向量
上的投影;
(2)求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5624d9561587784a272d3eff742d557d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106ff34d4ad867bc8def9d80aa328a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ec3efaa6b6ff5769e8999df5714a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d792a2aa25763e14cc2863be3887000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ec3efaa6b6ff5769e8999df5714a9.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
,
,
与
的夹角为
.
(1)求
在
方向上的投影;
(2)求
的值;
(3)若向量
与
的夹角是锐角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a18427949896e8c6073255731c84c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eca8fb20438505791369da9abe4a804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6849424bb49758b9c55fec214eef565.png)
(3)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b3f3bc84aa3bc6b032304ee5c072f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a4450297215b497e941afe092bb042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2021-03-25更新
|
1679次组卷
|
15卷引用:上海市南汇一中2018-2019学年高二上学期期中数学试题
上海市南汇一中2018-2019学年高二上学期期中数学试题上海市位育中学2017-2018学年高二第一学期期中考试数学试卷天津市静海区第一中学2019-2020学年高一下学期期中考试数学试题辽宁省锦州市黑山县黑山中学2019-2020学年高一6月质量检测数学试题(已下线)9.6 平面向量综合练习(提优)2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)第9章 平面向量 (B卷提升卷)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材苏教版)辽宁省六校协作体2020-2021学年高一下学期第三次联考数学试题湖南省常德市临澧县第一中学2019-2020学年高二下学期期中数学试题天津市经济技术开发区第一中学2020-2021学年高一下学期期中数学试题天津市北师大静海附属学校2020-2021学年高一下学期4月月考数学试题天津市第二南开学校2021-2022学年高一下学期期中数学试题云南省昭通市永善县知临中学2020-2021学年高一下学期期中数学模拟试题(2)天津市第四中学2022-2023学年高一下学期3月阶段性练习数学试题江苏省无锡市太湖高级中学2023-2024学年高一下学期3月月考数学试题山东省青岛市平度第一中学2023-2024学年高一下学期4月月考数学试题
名校
解题方法
4 . 双曲线
,圆
在第一象限交点为
,曲线
.
![](https://img.xkw.com/dksih/QBM/2021/1/4/2629059295584256/2629722248069120/STEM/5ba88b69-714b-4cea-b3cb-3b6f1e4c8d0c.png?resizew=244)
(1)若
,求b;
(2)若
,
与x轴交点记为
,P是曲线
上一点且在第一象限,并满足
,求∠
;
(3)过点
且斜率为
的直线
交曲线
于M、N两点,用b的代数式表示
,并求出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771f036702e7812030ead9a5ec6cd061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1777bb96c05fa932ef1ca5c716bc391e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4564dc28307341aea4003be38c19dfdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c194bc67a83a9b148e9c8e084a1740.png)
![](https://img.xkw.com/dksih/QBM/2021/1/4/2629059295584256/2629722248069120/STEM/5ba88b69-714b-4cea-b3cb-3b6f1e4c8d0c.png?resizew=244)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781e30964f70270f2cdf5d4c15ec3f1e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526d1c1f892971b9398ba764356dec3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45583fdd9864cc361ac09278f4f7241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05cb42d0a9194de4a06d4296ca5ae6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42144b85976d32be4536955fabc70b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e39f4de2b3e4010a4cfacd1d6342cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c58625fd2a35ef8883b60af16bf8926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c58625fd2a35ef8883b60af16bf8926.png)
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2021-01-05更新
|
1355次组卷
|
5卷引用:上海市建平中学2020-2021学年高二上学期12月月考数学试题
上海市建平中学2020-2021学年高二上学期12月月考数学试题2020年上海市高考数学练习(已下线)热点07 解析几何-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)考向11 正弦、余弦定理和解斜三角形-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)考向13 平面向量的数量积及应用-备战2022年高考数学一轮复习考点微专题(上海专用)
名校
解题方法
5 . 已知平面向量
与
,且
,
.
(1)求
与
的夹角;
(2)求
在
方向上的投影.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e310702748855c3edccd151aae0143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b574ac2684f90633174255c2125b6324.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bca35e52b8430246a1cf96e9e617cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
您最近一年使用:0次
名校
6 . 已知向量
和
的夹角为60°,且
,
.
(1)求向量
在
方向上的投影;
(2)若
,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3c6023f3ebdd4dca0c57b323531e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861e49ff83900da40ec23f4dda9eab11.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d258ac8d5b19539a90f9d445ea4980e.png)
您最近一年使用:0次
2020-01-16更新
|
181次组卷
|
2卷引用:上海市新场中学2020-2021学年高二上学期第二次月考(12月)数学试题
名校
7 . 已知
,
,且
与
的夹角为
,求:
(1)
在
上的投影;
(2)
;
(3)
与
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8faf351b569991fbdb8d8d30c72e72b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbcc0fa4b480c43e9a66273898c9a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44917f942c3fd36614f58d47b5fe1821.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cc8f1e4ec64189ce6b2400da174cf6.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614b003a9f14fed694128f681b2f1d91.png)
您最近一年使用:0次
2019-12-10更新
|
538次组卷
|
4卷引用:上海市上师大附中2018-2019学年高二上学期期中数学试题
8 . 已知向量
,向量
与向量
的夹角为
,且
,
(1)求向量
在向量
上的投影;
(2)求向量
的坐标;
(3)若
,
,
,其中A、C是△ABC的内角,若三角形的三内角A、B、C依次成等差数列,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26065fff3c4e0e259e6ab21bb6986106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12172a74a668b18236ba4e6d4569fd7c.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50482f7121a8d6d901c1a93e3514c4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6abb4d5e6622f480c196ba04727ec8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237513fa62c980d2196d57b0281b3887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b8dc2599cb77bbc1db851a98ea3014.png)
您最近一年使用:0次
名校
9 . 已知点
、
、
.
(1)若点
在第二或第三象限,且
,求
的取值范围;
(2)若
,
,
,求
在
方向上投影的取值范围;
(3)若
,求当
,且
的面积为
时,
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24705e5759ac944559f305c694c9f6d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091acaf5c3cbe20a5fff598323dc82be.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af733c6432ce382a8a3fc19ef315ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7556b085ed721d309c3376bf5e16ad21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1348dbdeba99934acf4cf5bc6b3bc5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36c9c91220b0f2cbd4a48e8fa90e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00da1c29aea46e36cda0f5780966bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe35c91649a5bea2518387a2b36e0c0d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b0b9a2c33a6b08e739435fc55e0f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c747e93ed8de8ad9b477e9c08c84441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4201d3bead2e48cc80052b1418f23db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
您最近一年使用:0次
2019-11-13更新
|
246次组卷
|
2卷引用:上海市高桥中学2017-2018学年高二上学期期中数学试题
10 . 已知
,
,
,且
.
(1)求向量
在向量
的方向上的投影;
(2)求实数
的值及向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4984318d967b210ce49f126794dad06b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab9ba8b25be6459228e9b50b90d91ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22943be0532cd5ff2a68a00de00af59d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac644684176e89d9605a49ab52dd1160.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c308ea87b699ee1dcb879a568899de.png)
您最近一年使用:0次