From fca2d6ce5d958a011d522ca4fc52f95b30bf53ba Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Sun, 4 Feb 2024 15:02:24 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=BA=8C=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A12?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 146 ++++++++++++++++++++++++++++++- 2 files changed, 148 insertions(+), 1 deletion(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 7ea7348f..16aeb4e4 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -352,3 +352,6 @@ 20240204-145635 高二寒假作业11 024547,003392,023692,024548:024556 +20240204-150205 高二寒假作业12 +030949,024557:024563,024434,003494 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 72b86946..3536d6d9 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -393081,7 +393081,9 @@ "20230128\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024561" + ], "remark": "", "space": "", "unrelated": [] @@ -664855,6 +664857,148 @@ "space": "4em", "unrelated": [] }, + "024557": { + "id": "024557", + "content": "如果向量 $\\overrightarrow{OA}=3 \\overrightarrow{i}+\\overrightarrow{j}-2 \\overrightarrow{k}$, $\\overrightarrow{OB}=-\\overrightarrow{i}+2 \\overrightarrow{j}-\\overrightarrow{k}$, $\\overrightarrow{OC}\\perp \\overrightarrow{OB}$, $\\overrightarrow{BC}\\parallel \\overrightarrow{OA}$, 那么向量 $\\overrightarrow{OC}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024558": { + "id": "024558", + "content": "已知点 $G$ 是 $\\triangle ABC$ 的重心, $O$ 是空间任一点, 若 $\\overrightarrow{OA}+\\overrightarrow{OB}+\\overrightarrow{OC}=\\lambda \\overrightarrow{OG}$, 则 $\\lambda$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024559": { + "id": "024559", + "content": "设 $A$、$B$、$C$、$D$ 是空间不共面的四点,\n且满足 $\\overrightarrow{AB}\\cdot \\overrightarrow{AC}=0$, $\\overrightarrow{AB}\\cdot \\overrightarrow{AD}=0$, $\\overrightarrow{AC}\\cdot \\overrightarrow{AD}=0$, 则 $\\triangle BCD$ 的形状为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024560": { + "id": "024560", + "content": "异面直线 $l_1, l_2$ 的方向向量分别为 $\\overrightarrow{d}_1, \\overrightarrow{d}_2$, 若 $\\cos \\langle\\overrightarrow{d}_1$, $\\overrightarrow{d}_2\\rangle=-\\dfrac{1}{2}$, 则 $l_1, l_2$ 所成角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024561": { + "id": "024561", + "content": "已知直线 $l_1, l_2$ 的方向向量分别为 $\\overrightarrow{d}_1, \\overrightarrow{d}_2$, 若 $\\overrightarrow{d_1}=(-1,0,1)$, $\\overrightarrow{d}_2=(1,1,-2)$, 则 $l_1, l_2$ 所成角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [ + "014040" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024562": { + "id": "024562", + "content": "直线 $l$ 的方向向量为 $\\overrightarrow{d}=(-1,1,2)$, 平面 $\\alpha$ 的法向量 $\\overrightarrow{n}=(2,1,-1)$, 则 $l$ 与平面 $\\alpha$ 所成角的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024563": { + "id": "024563", + "content": "二面角 $\\alpha-l-\\beta$ 的平面角为锐角, $\\alpha, \\beta$ 的法向量分别 $\\overrightarrow{n_1}=(1,0,0)$, $\\overrightarrow{n_2}=(-1,2,2)$, 则二面角 $\\alpha-l-\\beta$ 的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240204\t杨懿荔" + ], + "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