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收录高三寒假作业35新题

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wangweiye7840 2024-01-25 11:55:58 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -103,3 +103,6 @@
20240125-115315
023889:023896
20240125-115551
023897:023905

192
题库0.3/Problems.json
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@ -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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",