From 7f2bd5a45bc8040d270fbd3eb55436fedaab43eb Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 11:58:18 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A36=E6=96=B0=E9=A2=98?= 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 | 117 ++++++++++++++++++++++++++++++- 2 files changed, 117 insertions(+), 3 deletions(-) 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 8d620cdb..ebdd6598 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 @@ -106,3 +106,6 @@ 20240125-115551 023897:023905 +20240125-115808 +023906:023910,023151 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index cf3cbf84..1e9edb12 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -64463,7 +64463,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023907" + ], "remark": "", "space": "", "unrelated": [] @@ -64520,7 +64522,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023906" + ], "remark": "", "space": "", "unrelated": [] @@ -596129,7 +596133,9 @@ "20230319\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023906" + ], "remark": "", "space": "4em", "unrelated": [] @@ -644730,6 +644736,111 @@ "space": "4em", "unrelated": [] }, + "023906": { + "id": "023906", + "content": "若 $A(1,0,0)$、$B(0,2,0)$、$C(0,0,3)$ 为空间三点, 则平面 $ABC$ 的一个法向量为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "022074", + "001975" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023907": { + "id": "023907", + "content": "设平面 $\\alpha$ 的一个法向量为 $\\overrightarrow{n}=(-1,2,4)$, 直线 $l$ 的一个方向向量为 $\\overrightarrow{d}=(x, y, z)$.\\\\\n(1) 当 $l \\parallel $ 平面 $\\alpha$ 时, $x, y, z$ 满足\\blank{50};\\\\\n(2) 当 $l \\perp$ 平面 $\\alpha$ 时, $x, y, z$ 满足\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "001973" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023908": { + "id": "023908", + "content": "``直线的方向向量与平面的法向量垂直''是``直线与平面平行''的\\blank{50}条件.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023909": { + "id": "023909", + "content": "异面直线所成的角 $\\theta$ 与它们方向向量的夹角 $\\varphi$ 之间的关系为\\blank{50}; 直线与平面所成的角 $\\theta$ 与直线方向向量和平面法向量的夹角 $\\varphi$ 之间的关系为\\blank{50}; 二面角的大小 $\\theta$ 与两平面法向量的夹角 $\\varphi$ 之间的关系为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023910": { + "id": "023910", + "content": "如图所示是一个直三棱柱 (以 $A_1B_1C_1$ 为底面) 被一平面所截得到的几何体, 截面为 $ABC$. 已知 $A_1B_1=B_1C_1=1$, $\\angle A_1B_1C_1=90^{\\circ}$, $AA_1=4$, $BB_1=2$, $CC_1=3$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw ({-sqrt(2)/2},0,0) node [left] {$A_1$} coordinate (A_1);\n\\draw ({sqrt(2)/2},0,0) node [right] {$C_1$} coordinate (C_1);\n\\draw (0,0,{sqrt(2)/2}) node [below] {$B_1$} coordinate (B_1);\n\\draw (A_1) ++ (0,4,0) node [left] {$A$} coordinate (A);\n\\draw (B_1) ++ (0,2,0) node [right] {$B$} coordinate (B);\n\\draw (C_1) ++ (0,3,0) node [right] {$C$} coordinate (C);\n\\draw ($(A)!0.5!(B)$) node [below right] {$O$} coordinate (O);\n\\draw (A_1)--(B_1)--(C_1)--(C)--(A)--cycle(A)--(B)--(C)(O)--(C)(B)--(B_1);\n\\draw [dashed] (A_1)--(C_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 设点 $O$ 是 $AB$ 的中点, 证明: $OC \\parallel $ 平面 $A_1B_1C_1$;\\\\\n(2) 求二面角 $B-AC-A_1$ 的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "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