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修改23628题面

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weiye.wang 2024-02-15 13:12:13 +08:00
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10
题库0.3/Problems.json
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@ -644846,24 +644846,26 @@
},
"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{$|\\overrightarrow{c}|=|\\overrightarrow{d}|$}{$\\overrightarrow{a}\\cdot \\overrightarrow{b}=\\overrightarrow{a}\\cdot \\overrightarrow{c}$}{$\\overrightarrow{d}=\\dfrac{\\sqrt{3}}{3}\\overrightarrow{b}$}{$\\overrightarrow{c}\\cdot \\overrightarrow{d}=-\\dfrac{\\sqrt{3}}{9}$}",
"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\\blank{50}(填上所有你认为正确的选项).\\\\\n\\textcircled{1} $|\\overrightarrow{c}|=|\\overrightarrow{d}|$; \\textcircled{2} $\\overrightarrow{a}\\cdot \\overrightarrow{b}=\\overrightarrow{a}\\cdot \\overrightarrow{c}$; \\textcircled{3} $\\overrightarrow{d}=\\dfrac{\\sqrt{3}}{3}\\overrightarrow{b}$; \\textcircled{4} $\\overrightarrow{c}\\cdot \\overrightarrow{d}=-\\dfrac{\\sqrt{3}}{9}$.",
"objs": [],
"tags": [
"第五单元"
],
"genre": "解答题",
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240122\t赵琍琍"
"20240122\t赵琍琍",
"20240215\t王伟叶",
"20240215\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"space": "",
"unrelated": []
},
"023629": {