已知
,
,
.
(1)求
与
的夹角;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4244dd3d11b8c8131ffecd896c12a27c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bbe4fd72e48f10e4600e803d4ff61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31b7ec7a3d9d23cc283ac60d148531b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c250094127e2b3c878d68213b60407.png)
更新时间:2022-07-06 17:01:07
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相似题推荐
解答题-问答题
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适中
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解题方法
【推荐1】
的内角为A,B,C,
边上的高为
.
(1)用
表示
;
(2)若E为
边上一点,且
,试确定E点的位置,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccd5af8518c3021a065c4383783076f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbef69bb5ce04abc8a2daaf8da00d9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
(2)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cc79091dd7796a87ad51e61079fe5d.png)
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【推荐2】已知
.
(1)求
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3423888606fd127cbf6006cbac8bcb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb66f3b9440a15fc07b151e17c5328.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2439fff5870173794ce46ff7a9bfa206.png)
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【推荐3】如图,在边长为4的正三角形
中,
为
的中点,
为
中点,
,令
,
.
表示向量
;
(2)求
的值.
(3)延长线段
交
于
,设
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4c928019133a5d90cd602b6c0a4cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de92206d9c5afc2056f16086346a877e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dfbe48e1b5e6d747134bbf9ff0a97a.png)
(3)延长线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f85edf697138a58f99f82ebedbba6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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【推荐1】(1)已知向量
,
不共线,向量
,
,
,若A,
,
三点共线,求实数
的值;
(2)已知
,
,
,求
.
![](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/1f550135e4dfff8960d141c783e90156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557bd4a73f857593b788af42f55534c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c96ae526343ad98976789c91bccf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787379f7ff8d24be7eebfea1cfe956d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407538138dd68ab917925c2063cc98e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02accce5443c316768a4860a2bf4be1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93d44b4d52be5819b69956166134e90.png)
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【推荐2】如图,在
中,
,点E为AC中点,点F为BC上的三等分点,且靠近点C,设
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/18/5bffe54f-8e14-4d81-896d-4fdc35f7c7d6.png?resizew=170)
(1)用
,
表示
,
.
(2)若
,且
,求BC的长.
(3)若EF与CD交于点G,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0019a40382ab3b0ed0b127f75eabe48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad2785c82f621c4b807bb9a2493c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a6facc3f8956c8fea30f60455804f1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/18/5bffe54f-8e14-4d81-896d-4fdc35f7c7d6.png?resizew=170)
(1)用
![](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/bc1070a28cb9cb8553c29747d1993b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316c97c5b6f7c0fbdf7b9e4b9fccb661.png)
(3)若EF与CD交于点G,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46da4c5a4b5156f8ea762553d8ed0d18.png)
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【推荐1】已知平行四边形
中,E是
的中点,F是
边上靠近点B的三等分点,
与
交于点M,
,设
,且
.
(1)用
表示
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf80b036459da6dcb841a4bbe3859fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1aa922b038bd7247741f895e192568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d973a446723058aa19f043785c531c09.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b89403a4db68423b83136d2cbff6225.png)
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【推荐2】记
的内角
、
、
的对边分别为
、
、
,已知
,
.
(1)若
,
,求
;
(2)若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9941d6dacd8ccf0742471c9bda65eca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b655bd5572b287423444343d9428662f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0274a62d991a61c2a21e906f898bfb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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【推荐3】如图,在边长为2的等边三角形
中,D是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/360aeaf8-1458-4f01-b8aa-a1845b6971fb.png?resizew=142)
(1)求向量
与向量
的夹角;
(2)若O是线段
上任意一点,求
的最小值;
(3)通过本题的解答,试总结利用平面向量解决平面问题的基本方法
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/360aeaf8-1458-4f01-b8aa-a1845b6971fb.png?resizew=142)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a7f07db2ec637baadf8f0ab91c85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfff89daefe0c36b444d4e971deb057.png)
(2)若O是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0ba14e41e306e5633ad4bf1cdedd8.png)
(3)通过本题的解答,试总结利用平面向量解决平面问题的基本方法
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