1 . 下列命题中,
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb259bd6064946492bde050ec5a9053f.png)
②若
,
满足
,且
与
同向,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e2533f07582599408157d872d257dd.png)
③若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c217d19068e0194986a989da93ffdde7.png)
④若
是等边三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0e0035199419406ee67ebe79f62648.png)
其中正确的是_________ .(填写序号)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb259bd6064946492bde050ec5a9053f.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86ffae1773ae40b86cfc25d385f2eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e2533f07582599408157d872d257dd.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2720cbf09c689432bac86dd2d26fca1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c217d19068e0194986a989da93ffdde7.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0e0035199419406ee67ebe79f62648.png)
其中正确的是
您最近一年使用:0次
名校
2 . 已知向量
满足
(
为非零的实数),设向量
的夹角为
,有下列四个命题.其中正确的命题有___________ (填写所有正确结论的编号).
①存在
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98c41072ee589f5067938c658884541.png)
②不存在
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7557713682c09ec526718378189f9f7e.png)
③当
变化时,
的最大值为1
④当
变化时,
的最小值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96022a881e03e32d3483d997c3f170c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7529ee92d5e92360480ca8f87c15fdb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de631112eb0f79150eb75576090848c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98c41072ee589f5067938c658884541.png)
②不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7557713682c09ec526718378189f9f7e.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
您最近一年使用:0次
3 . 已知
、
、
分别是
的边
、
、
的中点,
为
的外心,且
,给出下列等式:
①
;②
;③
;④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f4e38e6d3af5df881e5b821e1c3884.png)
其中正确的等式是_________ (填写所有正确等式的编号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.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/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c607ac6de93e48cfe1805a5b61ba1528.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e9797890bf26b0ac59fc8bf2f78ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90af074d599eb5e01bd70c006eba18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8932a2f36e78140b8d19f748f3af957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f4e38e6d3af5df881e5b821e1c3884.png)
其中正确的等式是
您最近一年使用:0次
解题方法
4 . 过抛物线
焦点
的直线与抛物线交于
两点,作
垂直抛物线的准线
于
,
为坐标原点,则下列结论正确的是_______ (填写序号).
①
;
②存在
,使得
成立;
③
;
④准线
上任意点
,都使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a8528cd0649f5a271a37f88ba532ba.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb35b2338cb644c9cc0000094ea63b23.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e902c3982957249ce719e9af7b98d292.png)
④准线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f387a4813c2ab2880cf66d768196c70.png)
您最近一年使用:0次