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修改18513题面和答案

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weiye.wang 2024-01-21 13:46:18 +08:00
parent 92faa9cf4f
commit a226e0086d
1 changed files with 4 additions and 3 deletions
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题库0.3/Problems.json
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@ -497544,19 +497544,20 @@
},
"018513": {
"id": "018513",
"content": "在$\\triangle ABC$中, 设$\\overrightarrow{CA}=\\overrightarrow {a}, \\overrightarrow{CB}=\\overrightarrow {b}$, 记$\\triangle ABC$的面积为$S$\n(1) 求证: $S=\\dfrac{1}{2} \\sqrt{|\\overrightarrow {a}|^2|\\overrightarrow {b}|^2-(\\overrightarrow {a} \\cdot \\overrightarrow {b})^2}$;\n(2)设$\\overrightarrow {a}=(x_1, y_1), \\overrightarrow {b}=(x_2, y_2)$, 求证: $S=\\dfrac{1}{2}|x_1 y_2-x_2 y_1|$.\n$\\overrightarrow{OC} \\perp$. 设$OA$、$B$、$C$是平面上四点, 已知$\\overrightarrow{OA} \\perp \\overrightarrow{BC}, \\overrightarrow{OB} \\perp \\overrightarrow{AC}$. 求证:",
"content": "在$\\triangle ABC$中, 设$\\overrightarrow{CA}=\\overrightarrow {a}, \\overrightarrow{CB}=\\overrightarrow {b}$, 记$\\triangle ABC$的面积为$S$.\\\\\n(1) 求证: $S=\\dfrac{1}{2} \\sqrt{|\\overrightarrow {a}|^2|\\overrightarrow {b}|^2-(\\overrightarrow {a} \\cdot \\overrightarrow {b})^2}$;\\\\\n(2) 设$\\overrightarrow {a}=(x_1, y_1), \\overrightarrow {b}=(x_2, y_2)$, 求证: $S=\\dfrac{1}{2}|x_1 y_2-x_2 y_1|$.",
"objs": [],
"tags": [
"第五单元"
],
"genre": "解答题",
"ans": "",
"ans": "证明略; 证明略",
"solution": "",
"duration": -1,
"usages": [],
"origin": "空中课堂必修第二册平面向量例题与习题",
"edit": [
"20230705\t王伟叶"
"20230705\t王伟叶",
"20240121\t王伟叶"
],
"same": [],
"related": [],