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 87332be5..8d620cdb 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 @@ -103,3 +103,6 @@ 20240125-115315 023889:023896 +20240125-115551 +023897:023905 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 751c8633..cf3cbf84 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -460329,7 +460329,9 @@ "20230503\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023898" + ], "remark": "", "space": "4em", "unrelated": [] @@ -485817,7 +485819,9 @@ "20230606\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023903" + ], "remark": "", "space": "", "unrelated": [] @@ -644542,6 +644546,190 @@ "space": "4em", "unrelated": [] }, + "023897": { + "id": "023897", + "content": "设 $\\theta \\in \\mathbf{R}$. 若 $A(3 \\cos \\theta, 0,1)$、$B(3 \\sin \\theta, 1,1)$, 则 $|\\overrightarrow{AB}|$ 的取值范围是\\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": [] + }, + "023898": { + "id": "023898", + "content": "空间三点 $P(-2,0,2)$、$Q(-1,1,2)$、$R(-3,0,4)$, 则 $\\overrightarrow{PQ}$ 与 $\\overrightarrow{PR}$ 的夹角为\\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": [ + "016844" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023899": { + "id": "023899", + "content": "已知向量 $\\overrightarrow{a}=(x+3, y+1,3 x+2)$, $\\overrightarrow{b}=(2,0,5)$, 若 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, 则 $x=$\\blank{50}, $y=$\\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": [] + }, + "023900": { + "id": "023900", + "content": "已知向量 $\\overrightarrow{a}=(1,-1,2)$, 向量 $\\overrightarrow{AB}$ 与 $\\overrightarrow{a}$ 平行且 $|\\overrightarrow{AB}|=2 \\sqrt{6}$, 则 $\\overrightarrow{AB}=$\\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": [] + }, + "023901": { + "id": "023901", + "content": "已知向量 $\\overrightarrow{a}=(-1,0,1)$, $\\overrightarrow{b}=(1,2,3)$, 若 $k \\overrightarrow{a}-\\overrightarrow{b}$ 与 $\\overrightarrow{b}$ 垂直, 则实数 $k=$\\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": [] + }, + "023902": { + "id": "023902", + "content": "已知三个力 $\\overrightarrow{OF}_1=(1,2,3)$, $\\overrightarrow{OF}_2=(-2,3,-1)$, $\\overrightarrow{OF}_3=(3,-4,5)$, 若三个力作用于同一物体, 使物体从点 $M_1(1,-2,1)$ 移动到 $M_2(3,1,2)$, 则合力所作的功为\\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": [] + }, + "023903": { + "id": "023903", + "content": "已知 $A$、$B$、$C$ 三点不共线, $O$ 为平面 $ABC$ 外一点, 下列条件中能确定 $P$、$A$、$B$、$C$ 四点共面的是\\bracket{20}.\n\\twoch{$\\overrightarrow{OP}=\\overrightarrow{OA}+\\overrightarrow{OB}+\\overrightarrow{OC}$}{$\\overrightarrow{OP}=2 \\overrightarrow{OA}-\\overrightarrow{OB}-\\overrightarrow{OC}$}{$\\overrightarrow{OP}=\\dfrac{1}{5}\\overrightarrow{OA}+\\dfrac{1}{3}\\overrightarrow{OB}+\\dfrac{1}{2}\\overrightarrow{OC}$}{$\\overrightarrow{OP}=\\dfrac{1}{3}\\overrightarrow{OA}+\\dfrac{1}{3}\\overrightarrow{OB}+\\dfrac{1}{3}\\overrightarrow{OC}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "017984" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023904": { + "id": "023904", + "content": "与向量 $\\overrightarrow{AB}=(-4,6,-1)$, $\\overrightarrow{AC}=(4,3,-2)$ 都垂直的单位向量的坐标为\\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": [] + }, + "023905": { + "id": "023905", + "content": "(1) 设 $m, n \\in \\mathbf{R}$. 若 $A(-1,2,3)$、$B(2,1,4)$、$C(m, n, 1)$ 三点共线, 求 $m+n$ 的值;\\\\\n(2) 已知向量 $\\overrightarrow{a}=(2,-1,3)$, $\\overrightarrow{b}=(-1,4,-2)$, $\\overrightarrow{c}=(7,5, \\lambda)$ 共面, 求实数 $\\lambda$ 的值.", + "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