名校
解题方法
1 . 已知平面向量
其中
.
(1)若
,且
,求向量
的坐标;
(2)若向量
,若
与
垂直,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba55056a7121491bca24e0c6cc5c4d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8bc5db3d1568ef8ca089cf31e239bd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889b5481a226911819ede874f39279c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031bbd3b34b1c4e47f428e3f9b3787bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a22e6bf596853ef3132a6dc37731f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83c5803cc8c05849028a57c4bd4ee72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d5fa4100a6b6e8e2c3605c97e6ee78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c437edd4d400b1fc590f01652621273d.png)
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2 . 已知
,
,
与
的夹角为
.
(1)求
;
(2)求
与
夹角的余弦值;
(3)若
,
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ae0d7b3266f32b6a916b6237b6b838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b113dc271cf51b3018bd1de14edf73ad.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/d9cbb1eec186a57915e5aced5edce78c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea7e9c354c3e704c6f8ed02de9c2dda.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f0484158c0bb8ef08faf224bba82e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83c5803cc8c05849028a57c4bd4ee72.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f219540d81398b43c1336a8504e857a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5480b4d197235d88c618c52cb8cd01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
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7日内更新
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516次组卷
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3卷引用:黑龙江省佳木斯市第一中学2023-2024学年高一下学期5月期中考试数学试题
黑龙江省佳木斯市第一中学2023-2024学年高一下学期5月期中考试数学试题(已下线)【高一模块二】类型1 以平面向量为背景的解答题(A卷基础卷)福建省部分优质高中2023-2024学年高一下学期第二次阶段性检测数学试题
名校
3 . 在
中,
为
的中点,
为边
上的中点,
交
于
,设
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.png)
,
表示
;
(2)若
,
,
,求
的余弦值
(3)若
在
上,且
,设
,
,
,若
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.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/9cd5844deaa2a8cdda9477bcbf76c459.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede13546f2d31024998fd9a81b6004eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0f8a493ac2b5d05c09e47ed4169629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99db7cd00a7debcdd17f4716ba9cd77c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72689e44ff4e828835ee13ea82320fc6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5e19562bf0b7f47fa50b428d4c9f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede13546f2d31024998fd9a81b6004eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0f8a493ac2b5d05c09e47ed4169629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5685770f82fd0a654c6098caa53e6949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5610dc0acc42d3c5e5c60847842f7254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc53d9b451ff0fac9e1eb843eadfe33.png)
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解题方法
4 . 已知
,
,
,求:
(1)
;
(2)
与
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7958a6bddd1d578bbd6fbcb92e3f6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/190efc599b93baddd642ed5e2fcbcdaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594d993556173ded55043c25230776b2.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e6f98f23fea7db0f74897928024ca0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed492f7b29166ba5c1f0023b05a439c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3143307ad0ba4a631eac04e814993655.png)
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2024-05-29更新
|
617次组卷
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5卷引用:黑龙江省大庆市大庆中学2023-2024学年高一上学期月考数学试题
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5 . 已知
,
,
,
,
.
(1)若点D在第一、三象限的角平分线上,求
的值;
(2)若点D为线段BC的一个三等分点,求D的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d31cd03879d5c69ff11d0923f1ee82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7089a4e568ed92b1230af589f4d47be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208d21b0e0763afaa4dbad65adc77de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e87088da41685cc8d433fbbe0e18d6.png)
(1)若点D在第一、三象限的角平分线上,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若点D为线段BC的一个三等分点,求D的坐标.
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解题方法
6 . 已知向量
与
的夹角为
.
(1)求
的值;
(2)若
,求
在
上的投影向量
的坐标.
![](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/ecb6885c8c24e683798796ceaea3f9e4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b195aa36a3c2753ebf08cb464c52ad1e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208987bb884ab18a4f51911d75f1bc1e.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/d366d8fbb7258ee051f49977441e14a2.png)
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2024-05-08更新
|
1083次组卷
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3卷引用:黑龙江省绥化市绥棱县第一中学2023-2024学年高一下学期4月月考数学试题
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7 . 已知
为坐标原点,
,
,
.
(1)若
三点共线,求实数
的值;
(2)若点
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e717fc336c2b9c1617421b5b8a4ae6b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c052d7af2f98d95bac8725b608fba0fc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61eb783400ed8be99049a6d89fc21045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8b12e3bed2aff0970b56787253bc90.png)
您最近一年使用:0次
2024-05-08更新
|
236次组卷
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2卷引用:黑龙江省绥化市绥棱县第一中学2023-2024学年高一下学期4月月考数学试题
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8 . 已知函数
的部分图象如图所示.
的解析式;
(2)若
,求函数
在区间
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a28e06a36dc91105e73eddf7042db96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2605aa17904cd5b0c5f316a5e1d9f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172723002461ae60798317e2f10f6c2.png)
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9 . 已知
夹角为
,且
,求:
(1)
;
(2)
;
(3)
与
的夹角
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e906b18a41180399697862e474627b.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b195aa36a3c2753ebf08cb464c52ad1e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0081237674b159a7532c7f178986ce80.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e62efe57c935c50057c90ed8e45d387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8505aaf8a003faa6051bbd1edaa5ee91.png)
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10 . 水车是古代中国劳动人民发明的灌溉工具,相传为汉灵帝时华岚造出雏形,经三国时孔明改造完善后在蜀国推广使用.作为中国农耕文化的重要组成部分,它体现了中华民族的创造力,为中国农业文明和水利史研究提供了见证.被誉为“水车之都”的兰州建起了一处水车博览园,再现了以前黄河两岸水车林立的壮观景象.如图为一架新制作的水车,其最高点距离水面为18米,最低点在水面下2米,该水车每
转一圈,若从水轮左侧距离水面3米的点处开始计算时间(假定水车逆时针方向旋转).
距离水面的高度
(单位:
)表示为时间
(单位:
)的函数;
(2)在水轮转动的一圈内,有多长时间点
距水面的高度超过
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb21c93732b200bdddc5217b66090722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ce48eafd36547782174eb304d4a003.png)
(2)在水轮转动的一圈内,有多长时间点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e685c2fe2f54fa7947538472cd7caa9.png)
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