解题方法
1 . 用向量方法证明:菱形的两条对角线互相垂直.
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2 . 已知
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd9942eee66457a6e3f9d104addabbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afde30249b4bf49a03aa63f74888ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1c5bcaa260128e281a12f6ef6aacbc.png)
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2023-10-09更新
|
51次组卷
|
3卷引用:北师大版(2019)必修第二册课本习题第二章5.1向量的数量积
解题方法
3 . 求证:菱形的两条对角线互相垂直.
已知:如图,四边形ABCD是菱形.求证:
.
已知:如图,四边形ABCD是菱形.求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
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4 . 已知:
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25c4859f5c2a416bb175671e01aaf26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9063936d3b055420e5a7f16ee43e7ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c04d53c16732859c90332f61a6a5508.png)
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解题方法
5 . 已知
,
是夹角为
的两个单位向量,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3562008cf9f93fc603170229b4f43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9315c7eab43809baa7b62fc929d626c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
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解题方法
6 . 如图所示,已知
中,
分别为
边上的高,而且
与
相交于点O,连接
并延长,与
相交于点D.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5881068127a39caf319492b4177204f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
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2023-09-17更新
|
83次组卷
|
4卷引用:人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积 8.1.2 向量数量积的运算律
人教B版(2019) 必修第三册 逆袭之路 第八章 8.1 向量的数量积 8.1.2 向量数量积的运算律人教B版(2019)必修第三册课本例题8.1.2 向量数量积的运算律(已下线)6.2.4向量的数量积【第二练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)9.2 向量运算2 -【帮课堂】(苏教版2019必修第二册)
21-22高一·湖南·课后作业
7 . 设向量
,
,其中
.
(1)求证:
与
互相垂直;
(2)若
与
(其中
)大小相等,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb2a6ac6bb1cb11445577dd97e0fa30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5109992a5bf54faa23355741beb74959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b85478bd7295db8fbab462e5f9db1e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b91254db5ff748150f449c5cdd256c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1c1dd6b13d92f2cc2eef097e14c07c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41960bbc66bdc3b28be0138f83f9de5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496590f060e41cbaca42b9eaca3cc6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628560d39eeb0339fa00c9c15ab2c095.png)
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21-22高一·湖南·课后作业
8 . 如图,O为
的外心,以OA,OB为邻边作平行四边形,它的第四个顶点为点D,再以OC,OD为邻边作平行四边形,它的第四个顶点为点H.
,
,
,试用
,
,
表示
;
(2)在(1)的条件下,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9cb32a25c2a8bb99f75633b4cd5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049131856ba841523793ee3d83099014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eca8aa7145b2327dbccba46da05bb86.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/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a028159b675fb27a8ad3734c01841d26.png)
(2)在(1)的条件下,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4744b427f036dfbc6db68c87cd5c54.png)
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20-21高一·全国·课后作业
9 . 已知
,
是夹角为60°的两个单位向量,
,
.
(1)
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833e1932d717cb075f8f2c021b42981b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5bca280c9c9b8c3ad3849c06b1106fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28572bfb755a3e498822df1094b9df3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4f8922889c57c70c6fa4e46ab28e9d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0fe4d834e8eaca89ceaf9c64cdabd9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1cc86b7ff004a6ab4f88b7af2d58da.png)
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