名校
1 . 若对于向量
,
是一个单位向量,
,
与
的夹角为
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c734983e908fc8671cbf554aafe73aa.png)
![](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/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5ebbf3cdd35ccb6b77972401b07557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d4105cbfae0d960eba691fa2035ec8.png)
A.2 | B.1 | C.0 | D.![]() |
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2 . 在平面直角坐标系中,点
为原点,
.
(1)求
的坐标以及
的值;
(2)若
,且
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305ae9480d4bac4811a1de742a46972d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff19c492923bb47ef54de071c27e8c1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571b8a2416542301d1435a43a7de208e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e8e05917ce92f10501ee4b80d1edb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 下列各组向量中,可以作为基底的有( )
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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4 . 已知
是平面内两个不共线的向量,
,若
三点共线,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb371bd7728c6d6a16533a93924ad998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4468b444bac0675131e99c2e4e7fc4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.4 | C.![]() | D.0 |
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5 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e311ae799e3b4c00b8b888b219547f8.png)
A.![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.![]() ![]() ![]() |
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解题方法
6 . 已知
是两个单位向量,则以下四个结论中正确的是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 若向量
,
,满足
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219900a4325966330225c66942271030.png)
______ .
![](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/ede13546f2d31024998fd9a81b6004eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7af485413186ab3208767bc6637fb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b0093428ca3d3e314b89e108ca7cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219900a4325966330225c66942271030.png)
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解题方法
8 . 如图,在边长为3的等边三角形
中,
交
于点
点满足
,过
点的直线交
于点
,交
于点
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed5ea3e7db5a6943f2915d32339709c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6c45c4d19365b7928d81365585040.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e447c27b2e2acf936fa64e3a13bef727.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/18/45aa1023-0595-4d51-9839-0f0b9e482450.png?resizew=141)
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9 . 已知不共线的两个向量
,并且
.
(1)若
是
的中点,用
表示
;
(2)如果
,求
夹角
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af62a51e61a58e7fb5ff757d34695ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b80d9f86bc854bb2ff8680a6215bf4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af62a51e61a58e7fb5ff757d34695ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b797037bebb8966c497b52b21cae2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af62a51e61a58e7fb5ff757d34695ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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解题方法
10 . 在
中,已知
,若
为
内(含边界)一动点,
,则下列结论正确的是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ad269448978d4a3cdb5911c256a004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e535e5de14b757b47a1a001b675fdd.png)
A.若![]() ![]() | B.若![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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