1 . 设非零向量
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c367ebf81da8ce860b8d4db598ce3b0.png)
,并定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de1a1abedbffcec3416ebfbba00c22b.png)
(1)若
,求
;
(2)写出![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ee7554e993fa6d1035ea7da1621b6f.png)
之间的等量关系,并证明;
(3)若
,求证:集合
是有限集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b45cac4b26830e829a80640bf01673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c367ebf81da8ce860b8d4db598ce3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4776b8be0546414c6a82e0f7c21315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de1a1abedbffcec3416ebfbba00c22b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69cf5eb74f6f3b69186a665b06696d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9abc628cb2ec8b1250ac0e86a034611.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ee7554e993fa6d1035ea7da1621b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4776b8be0546414c6a82e0f7c21315.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fffedfb01c0a6802e19c44067252fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac41950e0db22f2216407b7e3999b51d.png)
您最近一年使用:0次
2023-07-25更新
|
468次组卷
|
3卷引用:北京市丰台区2022-2023学年高一下学期期末考试数学试卷
北京市丰台区2022-2023学年高一下学期期末考试数学试卷(已下线)专题07 向量应用-《重难点题型·高分突破》(苏教版2019必修第二册)【北京专用】专题06平面向量(第二部分)-高一下学期名校期末好题汇编
名校
2 . 已知函数
,若对于任意的实数
都能构成三角形的三条边长,则称函数
为
上的“完美三角形函数”.
(1)记
在
上的最大值、最小值分别为
,试判断“
”是“
为
上的“完美三角形函数”的什么条件?不需要证明;
(2)设向量
,若函数
为
上的“完美三角形函数”,求实数
的取值范围;
(3)已知函数
为
(
为正的实常数)上的“完美三角形函数”.函数
的图象上,是否存在不同的三个点
,它们在以
轴为实轴,
轴为虚轴的复平面上所对应的复数分别为
,满足
,且
?若存在,请求出相应的复数
,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7942abede925d39586071ad73e8c7de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237d8cd9bc612b6417614fbd70ee6c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b95e62946d710707f89d0c9f82c7ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02d5fbfa2feb617c6fabd1c35c5fb5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cf43aad35a9c6360908448b348be1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138ddbc9e4e842267a38425141063cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42017367e7f9fc70f99d70551852d6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2537912dc33dfc76ea1afa48c5d9e261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbc272e8a634e515c14f52bd64e84b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9246032f3154df10f63e03fef7ec5eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be94c746ea0cb4834e5295672e229a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2374bf53f7afc6eac3cf45d2befef826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a328844e8b5643eeda51d02c53bf248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be94c746ea0cb4834e5295672e229a4.png)
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名校
3 . 定义函数
的“源向量”为
,非零向量
的“伴随函数”为
,其中
为坐标原点.
的“伴随函数”为
,求
在
的值域;
(2)若函数
的“源向量”为
,且以
为圆心,
为半径的圆内切于正
(顶点
恰好在
轴的正半轴上),求证:
为定值;
(3)在
中,角
的对边分别为
,若函数
的“源向量”为
,且已知
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153386601e89709ded16e6e56cc86b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e80896903107cb0ec517fedffa3f735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e80896903107cb0ec517fedffa3f735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153386601e89709ded16e6e56cc86b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead0f45df9fc9e5a6a90a048daf15ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b0339e96e32d6fa1a092824850ef8d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6183bf0dcb6c744b27f6963007bda5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40589f60d5b9e76464c084d80fe92c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeca565ad5dfdba18cf431dd3b84c57e.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896785f1902334350af510775d152f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d76137ec77bd3221aa3842cabebe4910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3941f79eb3ae64e0f735ae45308e5b19.png)
您最近一年使用:0次
2024-04-07更新
|
728次组卷
|
2卷引用:重庆市巴蜀中学校2023-2024学年高一下学期3月月考数学试题
4 . 已知椭圆
,圆
.
(1)点
是椭圆
的下顶点,点
在椭圆
上,点
在圆
上(点
异于点
),连
,直线
与直线
的斜率分别记作
,若
,试判断直线
是否过定点?若过定点,请求出定点坐标;若不过定点,请说明理由.
(2)椭圆
的左、右顶点分别为点
,点
(异于顶点)在椭圆
上且位于
轴上方,连
分别交
轴于点
,点
在圆
上,求证:
的充要条件为
轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b1cb1359bcb061ce7737fb7e1b34f1.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa154ac33703b5c836047b2143697c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0aea8e4a6e524f43f9a13c1ef4fbddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f4fed042a050d47d7f1331605d7923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa0defb1d52e1973c1c6db736574dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c782675efb07943bcee0339945a08711.png)
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名校
5 . (1)利用向量的方法证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babd4243bfc7a34b7b4b4c45ea93b0ca.png)
(2)探索是否可以用向量法证明:在
中,若
,则
,若可以,请给出详细证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babd4243bfc7a34b7b4b4c45ea93b0ca.png)
(2)探索是否可以用向量法证明:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f2c59de12facaab92bcc74fbb42f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6eca11a1b3d037389bf029907c723de.png)
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6 . (1)证明:当
时,
;
(2)若过点
且斜率为
的直线
与曲线
交于
两点,
为坐标原点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468ddff079eafd5b6062e230f8ed42a.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0482468ee9123843cc9310b1fd7a27b4.png)
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解题方法
7 . 已知椭圆
,
是椭圆上的两个不同的点,
为坐标原点,
三点不共线,记
的面积为
.
(1)若
,求证:
;
(2)记直线
的斜率为
,当
时,试探究
是否为定值并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117de32547b9d58f3d102ec4c9b3bfc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/21/ba783b5d-4619-4335-aad4-d58e1e2a617c.png?resizew=213)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7332a5f0775000d42536c39a414fb66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7e00545464c5bb080ab5ddf22bf491.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac9ba606fb477550aa62db7bfa0ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5263f41aa7aa7a5ecbaed1a0a19c4f5d.png)
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8 . 过
的直线与
交于
,
两点,直线
、
与
分别交于
、
.
(1)证明:
中点在
轴上;
(2)若
、
、
、
四点共圆,求
所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c02130f82b629fab2c361dec15d41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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9 . 设平面向量
、
的夹角为
,
.已知
,
,
.
(1)求
的解析式;
(2)若
﹐证明:不等式
在
上恒成立.
![](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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956879af388928628970155bdb5c2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8e69e4abd4e261077ed177c25ff74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e074c209d628251349ecb15d76dfaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafdd5eff594c3ac6bc585b05c644fe5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bcd4e186c9b564603e00e4dfd0e8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe58c11b71e0ce7e6263b8112aa6140c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51742bc5df0b18cd3a6ca5abfb373bcc.png)
您最近一年使用:0次
2023-06-28更新
|
405次组卷
|
3卷引用:四川省达州市2022-2023学年高一下学期期末数学试题
名校
解题方法
10 . 若点P为
所在平面内一点,且
,则点P叫做
的费马点.当三角形的最大角小于
时,可以证明费马点就是“到三角形的三个顶点的距离之和最小的点”,即
最小.已知点O是边长为2的正
的费马点,D为BC的中点,E为BO的中点,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eab88a16df610f20dd46a44ba098d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed53a398b1d6b7b4abbb43a9abcf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2372bef75fa2ba16e360b552fcf6cd.png)
您最近一年使用:0次
2023-05-20更新
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1053次组卷
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7卷引用:辽宁省辽东区域教育科研共同体2022-2023学年高一下学期期中考试数学试题
辽宁省辽东区域教育科研共同体2022-2023学年高一下学期期中考试数学试题上海市华东师范大学第三附属中学2022-2023学年高一下学期期末数学试题(已下线)第五篇 向量与几何 专题15 几何最值(费马点、布洛卡点等) 微点3 费马点、布洛卡点综合训练(已下线)专题01 平面向量压轴题(1)-【常考压轴题】(已下线)6.3.5 平面向量数量积的坐标表示——课后作业(提升版)(已下线)8.2 向量的数量积-同步精品课堂(沪教版2020必修第二册)广西南宁市第二中学2023-2024学年高一下学期5月月考数学试卷