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收录高二寒假作业12

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wangweiye7840 2024-02-04 15:02:24 +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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@ -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

146
题库0.3/Problems.json
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@ -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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",