From a7afa0738bae34ae02fc3b8283b93a7ad8bdc9ed Mon Sep 17 00:00:00 2001
From: wangweiye7840 <kj_wangweiye@126.com>
Date: Mon, 22 Jan 2024 11:27:15 +0800
Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E5=9B=9B=E9=81=93=E8=87=AA?=
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---
 题库0.3/Problems.json | 80 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)

diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index ceee88c6..f03f8fb6 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -638715,6 +638715,86 @@
         "space": "4em",
         "unrelated": []
     },
+    "023628": {
+        "id": "023628",
+        "content": "已知 $\\overrightarrow{a}$、$\\overrightarrow{b}$ 为非零向量. 若 $\\overrightarrow{a}\\cdot \\overrightarrow{b}=-\\dfrac{\\sqrt{3}}{3}$, 向量 $\\overrightarrow{b}$ 在向量 $\\overrightarrow{a}$ 上的投影向量是 $\\overrightarrow{c}$, 向量 $\\overrightarrow{a}$ 在向量 $\\overrightarrow{b}$ 上的投影向量是 $\\overrightarrow{d}$, 则下列结论正确的是 (填上所有你认为正确的选项).\n\\fourch{$|\\overrightarrow{c}|=|\\overrightarrow{d}|$}{$\\overrightarrow{a}\\cdot \\overrightarrow{b}=\\overrightarrow{a}\\cdot \\overrightarrow{c}$}{$\\overrightarrow{d}=\\dfrac{\\sqrt{3}}{3}\\overrightarrow{b}$}{$\\overrightarrow{c}\\cdot \\overrightarrow{d}=-\\dfrac{\\sqrt{3}}{9}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240122\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023629": {
+        "id": "023629",
+        "content": "已知向量 $\\overrightarrow{a}$ 在向量 $\\overrightarrow{b}$ 上的投影向量的模是 $1$, 向量 $\\overrightarrow{b}$ 在向量 $\\overrightarrow{a}$ 上的投影向量的模是 $\\dfrac{1}{2}$, 且 $|\\overrightarrow{b}|=1$, 则 $|\\overrightarrow{a}-\\overrightarrow{b}|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240122\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023630": {
+        "id": "023630",
+        "content": "已知在平行四边形 $ABCD$ 中, $\\overrightarrow{DE}=\\dfrac{1}{2}\\overrightarrow{EC}$, $\\overrightarrow{BF}=\\dfrac{1}{2}\\overrightarrow{FC}$, $|\\overrightarrow{AE}|=2$, $|\\overrightarrow{AF}|=\\sqrt{6}$, 求 $\\overrightarrow{AC}\\cdot \\overrightarrow{DB}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240122\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023631": {
+        "id": "023631",
+        "content": "已知 $|\\overrightarrow{a}|=4$, $\\overrightarrow{e}$ 为单位向量, $\\langle\\overrightarrow{a}, \\overrightarrow{e}\\rangle=\\dfrac{2 \\pi}{3}$, 则向量 $\\overrightarrow{a}$ 在向量 $\\overrightarrow{e}$ 上的投影向量是\\blank{50}, 向量 $\\overrightarrow{e}$ 在向量 $\\overrightarrow{a}$ 上的投影向量是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240122\t赵琍琍"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",