From f50cc5c87c176c41099c9e2349910a85ae6e9e98 Mon Sep 17 00:00:00 2001
From: WangWeiye <kj_wangweiye@126.com>
Date: Tue, 16 May 2023 16:36:08 +0800
Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=80=E5=91=A8?=
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MIME-Version: 1.0
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---
 工具/修改题目数据库.py               |   2 +-
 工具/批量收录题目.py                 |  10 +-
 工具/文本文件/批量题目分类号记录.txt |   2 +
 题库0.3/Problems.json                | 740 +++++++++++++++++++++++++++
 4 files changed, 748 insertions(+), 6 deletions(-)

diff --git a/工具/修改题目数据库.py b/工具/修改题目数据库.py
index 413e2be8..9a1c2c6c 100644
--- a/工具/修改题目数据库.py
+++ b/工具/修改题目数据库.py
@@ -1,6 +1,6 @@
 import os,re,json
 """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块"""
-problems = "13480"
+problems = "40737,40738"
 
 def generate_number_set(string,dict):
     string = re.sub(r"[\n\s]","",string)
diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py
index 0569a7ec..c557cdad 100644
--- a/工具/批量收录题目.py
+++ b/工具/批量收录题目.py
@@ -1,9 +1,9 @@
 #修改起始id,出处,文件名
-starting_id = 17223
-raworigin = "2023届高三下学期月考2"
-filename = r"D:\temp\yuekao2.tex"
-editor = "20230507\t余利成"
-indexed = True
+starting_id = 40716
+raworigin = ""
+filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex"
+editor = "20230516\t王伟叶"
+indexed = False
 IndexDescription = "试题"
 
 import os,re,json
diff --git a/工具/文本文件/批量题目分类号记录.txt b/工具/文本文件/批量题目分类号记录.txt
index b996026d..bcb11a8c 100644
--- a/工具/文本文件/批量题目分类号记录.txt
+++ b/工具/文本文件/批量题目分类号记录.txt
@@ -214,10 +214,12 @@ problems_dict =  {
 "2025届高一下学期周末卷10":"40667:40686",
 "2025届高一下学期周末卷11":"40687:40706",
 "2025届高一下学期周末卷10与11小测":"40707:40715",
+"2025届高一下学期周末卷13":"40716:40737",
 "2025届高一下学期期中复习一(集合逻辑不等式)":"40283:40298",
 "2025届高一下学期期中复习二(幂指对函数)":"40368:40386",
 "2025届高一下学期测验01":"40336:40349",
 "2025届高一下学期测验02":"40350:40367",
+"2025届高一下学期测验03":"40738:40752",
 "2025届高一下学期区期中统考试题":"15269:15289",
 "2024届高二下学期周末卷01":"40001:40017",
 "2024届高二下学期周末卷02":"40037:40056",
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 8f035c55..c1446dff 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -546975,5 +546975,745 @@
         "remark": "",
         "space": "4em",
         "unrelated": []
+    },
+    "040716": {
+        "id": "040716",
+        "content": "若$\\overrightarrow{AB}=(2,4)$, $\\overrightarrow{AC}=(1,3)$, 则$\\overrightarrow{BC}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040717": {
+        "id": "040717",
+        "content": "已知$P_1(2,-1)$, $P_2(0,5)$若点$P$在直线$P_1P_2$上, 且满足$|\\overrightarrow{P_1P_2}|=2|\\overrightarrow{PP_2}|$, 则$P$点的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040718": {
+        "id": "040718",
+        "content": "若三点$A(2,2)$、$B(a,0)$、$C(0,4)$共线, 则$a$的值等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040719": {
+        "id": "040719",
+        "content": "点$P$在平面上作匀速直线运动, 速度向量$\\overrightarrow {v}=(4,-3)$. 设开始时点$P$的坐标为$(-10,10)$, 则$5$秒后点$P$的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040720": {
+        "id": "040720",
+        "content": "在直角坐标平面上, $O$是原点, $\\overrightarrow{OA}=(2,-4)$, $\\overrightarrow{OB}=(-2,-2)$, 若$x \\overrightarrow{OA}+y \\overrightarrow{OB}=3 \\overrightarrow{AB}$, 则实数$x=$\\blank{50}, $y=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040721": {
+        "id": "040721",
+        "content": "若$\\overrightarrow {a}=(k^2+k-3) \\overrightarrow {i}+(1-k) \\overrightarrow {j}$, $\\overrightarrow {b}=-3 \\overrightarrow {i}+(k-1) \\overrightarrow {j}$, $\\overrightarrow {a}$和$\\overrightarrow {b}$平行, 则$k=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040722": {
+        "id": "040722",
+        "content": "已知点$A(1,0)$、$B(0,2)$、$C(-1,-2)$, 则以$A$、$B$、$C$为顶点的平行四边形的第四个顶点$D$的坐标\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040723": {
+        "id": "040723",
+        "content": "已知$\\overrightarrow {e_1}, \\overrightarrow {e_2}$是不平行的向量, 设$\\overrightarrow {a}=\\overrightarrow {e_1}+k \\overrightarrow {e_2}$, $\\overrightarrow {b}=k \\overrightarrow {e_1}+\\overrightarrow {e_2}$, 则$\\overrightarrow {a}$与$\\overrightarrow {b}$共线的一个充要条件是实数$k$等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040724": {
+        "id": "040724",
+        "content": "在$\\triangle ABC$中, $O$为中线$AM$上一个动点, 若$AM=2$, 则$\\overrightarrow{OA} \\cdot(\\overrightarrow{OB}+\\overrightarrow{OC})$的最小值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040725": {
+        "id": "040725",
+        "content": "直角坐标平面上三点$A(1,2)$、$B(3,-2)$、$C(9,7)$, 若$E$、$F$为线段$BC$的三等分点, 则$\\overrightarrow{AE} \\cdot \\overrightarrow{AF}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040726": {
+        "id": "040726",
+        "content": "设$P$是$\\triangle ABC$所在平面内的一点, $\\overrightarrow{BC}+\\overrightarrow{BA}=2 \\overrightarrow{BP}$, 则\\bracket{20}.\n\\fourch{$\\overrightarrow{PA}+\\overrightarrow{PB}=\\overrightarrow{0}$}{$\\overrightarrow{PC}+\\overrightarrow{PA}=\\overrightarrow{0}$}{$\\overrightarrow{PB}+\\overrightarrow{PC}=\\overrightarrow{0}$}{$\\overrightarrow{PA}+\\overrightarrow{PB}+\\overrightarrow{PC}=\\overrightarrow{0}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040727": {
+        "id": "040727",
+        "content": "如图, 在$\\triangle ABC$中, $\\angle ACB=90^{\\circ}$, $AB=5$, $BC=4$, $CA=3$, 点$D$是边$BC$的中点, 点$H$在$AB$上, $CH \\perp AB$, 则$\\overrightarrow{AD} \\cdot \\overrightarrow{CH}=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (5,0) node [below] {$B$} coordinate (B);\n\\draw ({9/5},{12/5}) node [above] {$C$} coordinate (C);\n\\draw ($(B)!0.5!(C)$) node [right] {$D$} coordinate (D);\n\\draw ({9/5},0) node [below] {$H$} coordinate (H);\n\\draw (A)--(B)--(C)--cycle(C)--(H)(A)--(D);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040728": {
+        "id": "040728",
+        "content": "$\\triangle ABC$中, $\\overrightarrow{AB}=(2,4)$, $\\overrightarrow{BC}=(-6,2)$, 则$\\triangle ABC$的面积是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040729": {
+        "id": "040729",
+        "content": "已知向量$\\overrightarrow{a}=(1,2), \\overrightarrow{b}=(2,-3)$. 若向量$\\overrightarrow{c}$满足$(\\overrightarrow{c}+\\overrightarrow{a})\\parallel \\overrightarrow{b}, \\overrightarrow{c} \\perp(\\overrightarrow{a}+\\overrightarrow{b})$, 则$\\overrightarrow {c}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040730": {
+        "id": "040730",
+        "content": "设$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$为同一平面内具有相同起点的任意三个非零向量, 且满足$\\overrightarrow {a}$与$\\overrightarrow {b}$不共线, $\\overrightarrow {a} \\perp \\overrightarrow {c}$, $|\\overrightarrow {a}|=|\\overrightarrow {c}|$, 则$|\\overrightarrow {b} \\cdot \\overrightarrow {c}|$的值一定等于\\bracket{20}.\n\\twoch{以$\\overrightarrow {a}, \\overrightarrow {b}$为邻边的平行四边形的面积}{以$\\overrightarrow {b}, \\overrightarrow {c}$为两边的三角形面积}{$\\overrightarrow {a}, \\overrightarrow {b}$为两边的三角形面积}{以$\\overrightarrow {b}, \\overrightarrow {c}$为邻边的平行四边形的面积}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040731": {
+        "id": "040731",
+        "content": "$O$是平面上一定点, $A,B,C$是平面上不共线的三点, 动点$P$满足$\\overrightarrow{OP}=\\overrightarrow{OA}+\\lambda(\\dfrac{\\overrightarrow{AB}}{|\\overrightarrow{AB}|}+\\dfrac{\\overrightarrow{AC}}{|\\overrightarrow{AC}|})$, $\\lambda \\in(0,+\\infty)$, \n则$P$的轨迹一定通过$\\triangle ABC$的\\bracket{20}.\n\\fourch{外心}{内心}{重心}{垂心}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040732": {
+        "id": "040732",
+        "content": "向量$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$以及$\\overrightarrow {b}-\\overrightarrow {c}$都是非零向量, 则``$\\overrightarrow {a} \\cdot \\overrightarrow {b}=\\overrightarrow {a} \\cdot \\overrightarrow {c} ''$是``$\\overrightarrow {a} \\perp(\\overrightarrow {b}-\\overrightarrow {c})$''的\\bracket{20}条件.\n\\fourch{充分不必要}{必要不充分}{充分必要}{既不充分又不必要}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040733": {
+        "id": "040733",
+        "content": "已知$|\\overrightarrow {a}|=3,|\\overrightarrow {b}|=4$. 若$\\overrightarrow {c}$使得$\\overrightarrow {a}+\\overrightarrow {b}+\\overrightarrow {c}=\\overrightarrow{0}$, 则$\\overrightarrow {a} \\cdot \\overrightarrow {b}+\\overrightarrow {b} \\cdot \\overrightarrow {c}+\\overrightarrow {c} \\cdot \\overrightarrow {a}$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040734": {
+        "id": "040734",
+        "content": "设$\\lambda$是正实数, $\\triangle ABC$所在平面上的三点$A_1, B_1, C_1$(与$A,B,C$共六点两两不重合)满足: $\\overrightarrow{AA_1}=\\lambda(\\overrightarrow{AB}+\\overrightarrow{AC})$, $\\overrightarrow{BB_1}=\\lambda(\\overrightarrow{BC}+\\overrightarrow{BA})$, $\\overrightarrow{CC_1}=\\lambda(\\overrightarrow{CA}+\\overrightarrow{CB})$. 若$\\triangle ABC$与$\\triangle A_1B_1C_1$的面积相等, 则$\\lambda$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040735": {
+        "id": "040735",
+        "content": "已知$|\\overrightarrow {a}|=1$, $|\\overrightarrow {b}|=1$, 且向量$\\overrightarrow {a}$与$\\overrightarrow {b}$的夹角为$\\dfrac{\\pi}{3}$.\\\\\n(1) 设$\\overrightarrow {x}=2 \\overrightarrow {a}-\\overrightarrow {b}$, $\\overrightarrow {y}=3 \\overrightarrow {b}-\\overrightarrow {a}$, 求$\\overrightarrow {x}$与$\\overrightarrow {y}$的夹角;\\\\\n(2) 若向量$\\overrightarrow {a}$与$\\overrightarrow {a}+k \\overrightarrow {b}$的夹角为锐角, 求实数$k$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040736": {
+        "id": "040736",
+        "content": "如图, $\\triangle AOE$和$\\triangle BOE$都是边长为$1$的等边三角形, 延长$OB$到$C$使$|BC|=t$($t>0$), 连$AC$交$BE$于$D$点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.6]\n\\draw [->] (-0.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (2,0) node [below] {$E$} coordinate (E);\n\\draw (60:2) node [above] {$A$} coordinate (A);\n\\draw (-60:2) node [below] {$B$} coordinate (B);\n\\draw ($(O)!1.3!(B)$) node [below] {$C$} coordinate (C);\n\\path [name path = AC] (A)--(C);\n\\path [name path = BE] (B)--(E);\n\\path [name intersections = {of = AC and BE, by = D}];\n\\draw (O)--(D) node [right] {$D$};\n\\draw (O)--(A)--(E)--(B)--cycle(A)--(C)(B)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 用$t$表示向量$\\overrightarrow{OC}$和$\\overrightarrow{OD}$的坐标\\\\\n(2) 求向量$\\overrightarrow{OD}$和$\\overrightarrow{EC}$的夹角的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040737": {
+        "id": "040737",
+        "content": "在同一个平面内, 有向量$\\overrightarrow {a}$、$\\overrightarrow {b}$、$\\overrightarrow {p}$、$\\overrightarrow {q}$、$\\overrightarrow {r}$, 其中$\\overrightarrow {b} \\neq \\overrightarrow{0}$, 且$\\overrightarrow {a} \\perp \\overrightarrow {b}$, $|\\overrightarrow {a}|=2|\\overrightarrow {b}|$.\\\\\n(1) 若$|\\overrightarrow {b}|=1$, 求$|\\overrightarrow {a}-\\overrightarrow {b}|$的值;\\\\\n(2) 设常数$k \\in \\mathbf{R}$. 若向量$\\overrightarrow {p}=k \\overrightarrow {a}+2 \\overrightarrow {b}$, $\\overrightarrow {q}=\\overrightarrow {a}+2 k \\overrightarrow {b}$, $\\overrightarrow {p}$与$\\overrightarrow {q}$的夹角大小为$120^{\\circ}$, 求$k$的值;\\\\\n(3) 设$\\overrightarrow {r} \\neq \\overrightarrow{0}$, 且$\\theta$是$\\overrightarrow {r}$与$\\overrightarrow {a}$的夹角. 若$\\overrightarrow {r} \\cdot \\overrightarrow {a}=\\overrightarrow {r} \\cdot \\overrightarrow {b}$, 求$\\theta$的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期周末卷13",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040738": {
+        "id": "040738",
+        "content": "若向量$\\overrightarrow {a}$、$\\overrightarrow {b}$满足$\\overrightarrow {a}+\\overrightarrow {b}=(2,-2)$, $\\overrightarrow {a}-\\overrightarrow {b}=(-2,4)$, 则$\\overrightarrow {a} \\cdot \\overrightarrow {b}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040739": {
+        "id": "040739",
+        "content": "若非零向量$\\overrightarrow {a}, \\overrightarrow {b}$满足$|\\overrightarrow {a}+\\overrightarrow {b}|=2|\\overrightarrow {a}|$, $|\\overrightarrow {b}|=\\sqrt{3}|\\overrightarrow {a}|$, 则$\\overrightarrow {a}$与$\\overrightarrow {b}$所成角的大小为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040740": {
+        "id": "040740",
+        "content": "若$|\\overrightarrow {a}|=1$, $|\\overrightarrow {b}|=3$, 且$\\overrightarrow {a}$与$\\overrightarrow {b}$的夹角为$\\dfrac{2 \\pi}{3}$, 则$|\\overrightarrow {a}-3 \\overrightarrow {b}|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040741": {
+        "id": "040741",
+        "content": "设向量$\\overrightarrow {a}=(2,3)$, 点$A$的坐标为$(1,4)$. 若向量$\\overrightarrow{AB}$与$\\overrightarrow {a}$方向相反, 且$|\\overrightarrow{AB}|=3|\\overrightarrow {a}|$, 则点$B$的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040742": {
+        "id": "040742",
+        "content": "已知向量$\\overrightarrow {p}=\\dfrac{\\overrightarrow {a}}{|\\overrightarrow {a}|}+\\dfrac{\\overrightarrow {b}}{|\\overrightarrow {b}|}$, 其中$\\overrightarrow {a}, \\overrightarrow {b}$均为非零向量, 则$|\\overrightarrow {p}|$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040743": {
+        "id": "040743",
+        "content": "已知向量$\\overrightarrow {a}=(1,2)$, $\\overrightarrow {b}=(2,-3)$, 若向量$\\overrightarrow {c}$满足$(\\overrightarrow {c}+\\overrightarrow {a})\\parallel \\overrightarrow {b}$, $\\overrightarrow {c} \\perp(\\overrightarrow {a}+\\overrightarrow {b})$, 则$\\overrightarrow {c}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040744": {
+        "id": "040744",
+        "content": "设$O$是坐标原点, $\\overrightarrow{OA}=(k, 12)$, $\\overrightarrow{OB}=(4,5)$, $\\overrightarrow{OC}=(10, k)$, 则$k=$\\blank{50}时, $A$、$B$、$C$三点共线.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040745": {
+        "id": "040745",
+        "content": "设$A(a, 1), B(2, b), C(4,5)$为坐标平面上三点, $O$为坐标原点, 若$\\overrightarrow{OA}$与$\\overrightarrow{OB}$在$\\overrightarrow{OC}$方向上的投影相同, 则$a$、$b$满足的关系是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040746": {
+        "id": "040746",
+        "content": "在$\\triangle ABC$中, $AD \\perp AB$, $\\overrightarrow{BC}=\\sqrt{3} \\overrightarrow{BD}$, $|\\overrightarrow{AD}|=1$($D$为垂足), 则$\\overrightarrow{AC} \\cdot \\overrightarrow{AD}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040747": {
+        "id": "040747",
+        "content": "设常数$t \\in \\mathbf{R}$, 向量$\\overrightarrow {a}=(2, t)$, $\\overrightarrow {b}=(-1,2)$. 若$\\overrightarrow {a}$与$\\overrightarrow {b}$的夹角为钝角, 则$t$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040748": {
+        "id": "040748",
+        "content": "设$\\overrightarrow {e_1}$、$\\overrightarrow {e_2}$为单位向量, 且$\\overrightarrow {e_1}$、$\\overrightarrow {e_2}$的夹角大小为$60^{\\circ}$. 若$\\overrightarrow {a}=\\overrightarrow {e_1}-\\overrightarrow {e_2}$, $\\overrightarrow {b}=2 \\overrightarrow {e_1}$, 则$\\overrightarrow {a}$在$\\overrightarrow {b}$方向上的数量投影为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040749": {
+        "id": "040749",
+        "content": "给定两个不平行的非零向量$\\overrightarrow{OA}$、$\\overrightarrow{OB}$, $M$是$OB$的中点, $N$是$AB$上靠近$B$的三等分点, 点$C$在$MN$上变动, 若$\\overrightarrow{OC}=x \\overrightarrow{OA}+y \\overrightarrow{OB}$, 其中$x$、$y \\in \\mathbf{R}$, 则$x+y$的范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "040750": {
+        "id": "040750",
+        "content": "已知两点$A(-1,2)$, $B(2,8)$, $C$、$D$两点满足$\\overrightarrow{AB} \\cdot \\overrightarrow{AC}=1$, $\\overrightarrow{OA} \\cdot(\\dfrac{1}{2} \\overrightarrow{BC})=0$, $\\overrightarrow{DC}+2 \\overrightarrow{AD}=0$, 求$C$、$D$两点的坐标(其中$O$是原点).",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040751": {
+        "id": "040751",
+        "content": "已知$|\\overrightarrow {a}|=1$, $|\\overrightarrow {b}|=2$, $\\overrightarrow {a}$、$\\overrightarrow {b}$的夹角为$\\dfrac{\\pi}{3}$, 记$\\overrightarrow {m}=3 \\overrightarrow {a}-\\overrightarrow {b}$, $\\overrightarrow {n}=2 \\overrightarrow {a}+2 \\overrightarrow {b}$, 求$\\overrightarrow {m}$与$\\overrightarrow {n}$的夹角.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "040752": {
+        "id": "040752",
+        "content": "设$t \\in \\mathbf{R}$,  $O(0,0)$, $A(1,2)$, $B(4,5)$, $C$四点满足$\\overrightarrow{OC}=\\overrightarrow{OA}+t \\overrightarrow{AB}$.\\\\\n(1) $t$为何值时, 点$C$在$y$轴上?\\\\\n(2) 四边形$OABC$能否成为平行四边形? 若能, 求出相应的$t$的值; 若不能, 请说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一下学期测验03",
+        "edit": [
+            "20230516\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
     }
 }
\ No newline at end of file