名校
解题方法
1 . 已知单位向量
,向量
与
不共线,且
,则
的最大值为______ .
![](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/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fafdbb4d89d56b7e7f5a93a4968987b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7d8b42c85013ba07ba18e5e46d8716.png)
您最近一年使用:0次
名校
解题方法
2 . 设O为坐标原点,
为双曲线
的两个焦点,点P在C上,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e72358a12f923519a407a46c07f5d33.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97027a5dd71bb14db141ae54ab6428e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6e794bb451146907682a411f3855aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e72358a12f923519a407a46c07f5d33.png)
您最近一年使用:0次
3 . 在
中,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bfb857a8c1af3f7980aebeda20b2a2.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054c47fe9b9dd25d0e1e7e7f3403c0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1bfb857a8c1af3f7980aebeda20b2a2.png)
您最近一年使用:0次
解题方法
4 . 在
中,已知
的对边分别为
为
延长线上一点,直线
平分
,且与直线
交于
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc73b98eb6edcdc04b7bb6b52a957f02.png)
__________ .
![](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/4f188b8527ef5ebc3671b21ba93f036c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5157b42da58d55daad27d98b2fec15ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc73b98eb6edcdc04b7bb6b52a957f02.png)
您最近一年使用:0次
解题方法
5 . 已知
是两个单位向量,若
在
上的投影向量为
,则
与
的夹角为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](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/62c86779e465e98e32df7e1de20a0a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0920be0508984a3c3a337b3a93c525c4.png)
您最近一年使用:0次
6 . 空间直角坐标系中,从原点出发的两个向量
、
满足:
,
,且存在实数
,使得
成立,则由
构成的空间几何体的体积是______ .
![](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/e37157acb52896b1d3d067adc7d381b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf342e77c56e55a35bb1151bc215a3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67cebb122295180866d58f6f409fdb9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
7 . 已知向量
满足
,向量
在向量
上的投影数量为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f57172fd74558544613e041158abdc.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d0692c60541a453ce8cc40c9ce9aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99d7b3100c85d37491eeb5dae4a8a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7a1df960feef63dec4790d63f52279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1b0f871d1189164bfcbbec8c77f9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f57172fd74558544613e041158abdc.png)
您最近一年使用:0次
解题方法
8 . 设
均为单位向量,且
可按一定顺序成等比数列,写出一个符合条件的
的值_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8002bd93f0d69a81ed5564c10d44571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
您最近一年使用:0次
解题方法
9 . 已知
、
是空间中两个互相垂直的单位向量,向量
满足
,且
,当
取任意实数时,
的最小值为_________ .
![](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/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1fa7538549bf04c02a09ead1745ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3652b4e7527892ec1ed1388f046f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c565a1ad173e90c48c56ecc26e384d99.png)
您最近一年使用:0次
10 . 已知
为椭圆
的两个焦点,
为原点,
为椭圆
上一点,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be68669e8cde95b6f844477a2acfb1e3.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7affd8a277498fd39b4a2a95d649f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be68669e8cde95b6f844477a2acfb1e3.png)
您最近一年使用:0次