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1 . 已知
若
则x=_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194748b2b8bd9f6b7af383577245fd4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44550cf9a8d26d7ba494e8111e487c74.png)
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3卷引用:广东省潮州市松昌中学2023-2024学年高一下学期期中考试数学试题
广东省潮州市松昌中学2023-2024学年高一下学期期中考试数学试题(已下线)专题01 平面向量(2)-期末考点大串讲(苏教版(2019))上海市闵行中学2023-2024学年高一下学期期末考试数学试卷
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2 . 已知正六棱柱的所有棱长均为2,则该正六棱柱的外接球的体积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 如图,一个几何体是由一个正三棱柱内挖去一个倒圆锥组成,该三棱柱的底面正三角形的边长为2,高为4.圆锥的底面内切于该三棱柱的上底面,顶点在三棱柱下底面的中心处.
(2)求该几何体的表面积.
(2)求该几何体的表面积.
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4 . 已知向量
,且
与
的夹角为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e3430cc976da11493e693783796939.png)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c9abe1f8fb33024df04558987daf1f.png)
(2)若
,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786954a4502555f3455f4a41df1b0786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fe4e713c108e118522a99ecd683924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ede7d953b17fc5153c45029218ecc83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e3430cc976da11493e693783796939.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c9abe1f8fb33024df04558987daf1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b190b5fb977d012e536ce8cfe6e430a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5 . 在
中,
为BC上一点,
是AD的中点,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](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/15c9acc8e0a6a969fa8227b84a088338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550329e53494cbcad81a474778ed3c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
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6 . 已知向量
、
,向量
平分
与
的夹角,则下列结论一定正确的是( )
![](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/ed492f7b29166ba5c1f0023b05a439c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 如图,已知
为平面直角坐标系的原点,
,
,则向量
在向量
上的投影向量为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f455353f09b4c255f8a5efeb72b9e93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be074751f43f67163a20e2f47d906715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
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8 . 设
、
分别是
的边
、
上的点,
,
,
.
(1)若
(
、
为实数),求
的值;
(2)若
(
、
为实数),求
的值.
![](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/15c0dbe3c080c4c4636c64803e5c1f76.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/f74a61581d965458316280968241e4c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f3ddfd586ae5432f0c06e5b1a76ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a936641949d6f9daa1e9bb2679b5fc1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cea8f02768bdd7e869290d042a5748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0ee8fc6d8bbd11a0cf66a86207bd69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061baa765d2939a416300de14c45b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf97cb5e2fa09745dbb21b9bcfe9e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698533f7cec9ad4a58bbf307bbdc93d5.png)
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9 . 已知
是虚数单位,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
A.![]() ![]() ![]() ![]() |
B.“![]() ![]() |
C.若复数![]() ![]() ![]() |
D.若复数![]() ![]() ![]() |
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10 . 作用于同一点
的三个力
处于平衡状态,已知
,
,
的夹角为
,则
与
夹角的大小为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d66f6559857f4e9b12e57c4bba39733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7df35a54f266e6a23af1007f0129f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca5ed80bcc316fd738cc9503f1a3877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4949a50a01625d2290cc5ef590e51d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8136e8bf2bde87aba070b76e3a3196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809f928a25b77674be3116e2e79e6c65.png)
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