1 . 如图,在边长为1的正六边形
中,
为边
上一点,且满足
,设
,
.
(1)若
,试用
,
表示
向量;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53e5ca390254ba5b125e8cdf8c51e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dbdda9fb5813e20558da8aeeee4b37.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d0c758006b3034b61c33e5f0cefb00.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed51e7bcf597ba87c23a6f6d2ef2c3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/8/e9490598-5899-400d-aaa6-b3f2fcd896c4.png?resizew=201)
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2 . 已知正三角形ABC边长为2,D是BC的中点,点E满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3721efcac061fe5a5367a03d087753df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed502d83b31e88a172e16eec88d2f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3721efcac061fe5a5367a03d087753df.png)
A.![]() | B.![]() | C.![]() | D.-1 |
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2019-09-08更新
|
434次组卷
|
3卷引用:江苏省南通市第一中学2019-2020学年高一上学期期末数学试题
名校
3 . 在△ABC中,AB=3,AC=2,∠BAC=120°,
.若
,则实数λ的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86c675cf50716ab7e3d0362855f466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc06a1bf3e7ebddde29cf1bdf1bf9308.png)
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2020-01-21更新
|
315次组卷
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9卷引用:江苏省南京市2018届高三上学期期初学情调研考试数学试题
江苏省南京市2018届高三上学期期初学情调研考试数学试题江苏省南京市2018届高三数学上学期期初学情调研考试数学试题江苏省南京外国语学校仙林分校中学部2017—2018学年度高二下学期期末测试(理科)数学试题江苏省南通市启东中学2018-2019学年高二上学期期初考试数学试题江苏省无锡市2018-2019学年高二下学期期末质量数学(文)试题(已下线)专题06 平面向量的应用-《巅峰冲刺2020年高考之二轮专项提升》(江苏)江苏省淮安市涟水县第一中学2019-2020学年高三上学期10月月考数学(文)试题山东省枣庄市第三中学2018-2019学年高一下学期6月月考数学试题(已下线)考点37 平面向量的应用-备战2022年高考数学一轮复习考点帮(新高考地区专用)【学科网名师堂】
12-13高三上·江苏扬州·阶段练习
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4 . 在△ABC中,已知BC=2,
,则△ABC面积的最大值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143e743575e406a4e5009c5727282417.png)
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2016-12-01更新
|
1401次组卷
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4卷引用:2012届江苏省扬州中学高三11月练习数学试卷
(已下线)2012届江苏省扬州中学高三11月练习数学试卷【全国百强校】江苏省海安中学2017-2018学年高一下学期期中考试数学试题(普通班)(已下线)2012-2013学年江西上饶横峰中学上学期高三第一次月考理科数学试卷上海交通大学附属中学2024届高三上学期10月月考数学试题
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5 . 如图,在平行四边形ABCD中,P,Q分别是BC和CD的中点.
![](https://img.xkw.com/dksih/QBM/2021/1/6/2630197904957440/2632908828786688/STEM/68db3f10a3444126a2cd842a2f95e8cd.png?resizew=154)
(1)若
,
,
,求
及
的余弦值;
(2)若
,求
的值.
![](https://img.xkw.com/dksih/QBM/2021/1/6/2630197904957440/2632908828786688/STEM/68db3f10a3444126a2cd842a2f95e8cd.png?resizew=154)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b89e7ff008dea7530bdc4ea5b6419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5cb63aeea0b37799404c8fec092b21d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5d4ad19f64c408b627ff9f6146a733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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2021-01-10更新
|
208次组卷
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2卷引用:江苏省吴江中学2020-2021学年高一下学期3月月考数学试题
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6 . 在
中,
,角
的平分线与
边上的中线交于点
,
,则
的值 ________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075c7c1a177dd21015775509836522e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/4bc09eb2433afa4df63252f6badfedff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e6508e26d0a1315131dfed21d8bb5a.png)
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7 . 已知
中.
(1)设
,求证:
是等腰三角形;
(2)设向量
,
,且
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e16aef8305c8c9097f215346602a49c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7539fe5bd18cdaf5fc48e97887519d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18db98d66df644722ccebc1d223eb74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccf7454c9e7dac9478eca82f709429c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de08e9e977f8997b0a7d351bf338c1fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46b9c5badc59f462e5f98d270a13f8f.png)
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8 . 平行四边形
中,
,
为平行四边形内一点,且
,若
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a608e2854920ddafa7feb19dd8e505bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae347d8a75aab356ad0f8cde35b6e2c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15baa70b055f1d23e99bc071637fc2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f716ed237de48f4d0d7a3613a14bee0.png)
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|
516次组卷
|
2卷引用:【全国百强校】江苏省海安高级中学2017-2018学年高二6月月考数学(理)试题
9 . 在平行四边形ABCD中,∠BAD=60°,AB=1,AD=
,P为平行四边形内一点,且AP=
,若
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62841fefbd483bedee4703ce6eccfab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55963dede1356480863a5624256576b8.png)
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2016-12-04更新
|
1097次组卷
|
3卷引用:2016届江苏省泰州市姜堰区高三下期初考试数学试卷
解题方法
10 . 如图,在四边形
中,对角线
与
相交于点
.已知
,
,
,且
是
的中点,若
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.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/cf1f5a142a64172a7f21123204104198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3728d1c17bd92866025193c752121a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/f369a36f-fd47-4da5-bd76-4fa704c875a2.png?resizew=174)
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