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录入四道自拟题目

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wangweiye7840 2024-01-22 11:27:15 +08:00
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题库0.3/Problems.json
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"space": "4em",
"unrelated": []
},
"023628": {
"id": "023628",
"content": "已知 $\\overrightarrow{a}$、$\\overrightarrow{b}$ 为非零向量. 若 $\\overrightarrow{a}\\cdot \\overrightarrow{b}=-\\dfrac{\\sqrt{3}}{3}$, 向量 $\\overrightarrow{b}$ 在向量 $\\overrightarrow{a}$ 上的投影向量是 $\\overrightarrow{c}$, 向量 $\\overrightarrow{a}$ 在向量 $\\overrightarrow{b}$ 上的投影向量是 $\\overrightarrow{d}$, 则下列结论正确的是 (填上所有你认为正确的选项).\n\\fourch{$|\\overrightarrow{c}|=|\\overrightarrow{d}|$}{$\\overrightarrow{a}\\cdot \\overrightarrow{b}=\\overrightarrow{a}\\cdot \\overrightarrow{c}$}{$\\overrightarrow{d}=\\dfrac{\\sqrt{3}}{3}\\overrightarrow{b}$}{$\\overrightarrow{c}\\cdot \\overrightarrow{d}=-\\dfrac{\\sqrt{3}}{9}$}",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240122\t赵琍琍"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"023629": {
"id": "023629",
"content": "已知向量 $\\overrightarrow{a}$ 在向量 $\\overrightarrow{b}$ 上的投影向量的模是 $1$, 向量 $\\overrightarrow{b}$ 在向量 $\\overrightarrow{a}$ 上的投影向量的模是 $\\dfrac{1}{2}$, 且 $|\\overrightarrow{b}|=1$, 则 $|\\overrightarrow{a}-\\overrightarrow{b}|=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240122\t赵琍琍"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"023630": {
"id": "023630",
"content": "已知在平行四边形 $ABCD$ 中, $\\overrightarrow{DE}=\\dfrac{1}{2}\\overrightarrow{EC}$, $\\overrightarrow{BF}=\\dfrac{1}{2}\\overrightarrow{FC}$, $|\\overrightarrow{AE}|=2$, $|\\overrightarrow{AF}|=\\sqrt{6}$, 求 $\\overrightarrow{AC}\\cdot \\overrightarrow{DB}$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240122\t赵琍琍"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"023631": {
"id": "023631",
"content": "已知 $|\\overrightarrow{a}|=4$, $\\overrightarrow{e}$ 为单位向量, $\\langle\\overrightarrow{a}, \\overrightarrow{e}\\rangle=\\dfrac{2 \\pi}{3}$, 则向量 $\\overrightarrow{a}$ 在向量 $\\overrightarrow{e}$ 上的投影向量是\\blank{50}, 向量 $\\overrightarrow{e}$ 在向量 $\\overrightarrow{a}$ 上的投影向量是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240122\t赵琍琍"
],
"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.",