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修改021770:021771,021775,021820题面

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weiye.wang 2024-02-24 13:05:22 +08:00
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题库0.3/Problems.json
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@ -592731,7 +592731,7 @@
},
"021770": {
"id": "021770",
"content": "在平行四边形$ABCD$中, $AD=1$, $\\angle BAD=60^{\\circ}$, $E$为$CD$的中点, 若$\\overrightarrow{AD} \\cdot \\overrightarrow{BE}=1$, 求$AB$的长.",
"content": "在平行四边形$ABCD$中, $AD=1$, $\\angle BAD=60^{\\circ}$, $E$为$CD$的中点, 若$\\overrightarrow{AD} \\cdot \\overrightarrow{BE}=-1$, 求$AB$的长.",
"objs": [],
"tags": [
"第五单元"
@ -592752,7 +592752,8 @@
],
"origin": "2025届高一下校本作业",
"edit": [
"20230209\t王伟叶"
"20230209\t王伟叶",
"20240224\t王伟叶"
],
"same": [],
"related": [],
@ -592762,7 +592763,7 @@
},
"021771": {
"id": "021771",
"content": "已知$\\overrightarrow {a} \\overrightarrow {b}$是两个不共线的向量, 若它们起点相同, $\\overrightarrow {a}$、$\\dfrac{\\overrightarrow {b}}{2}$、$t(\\overrightarrow {a}+\\overrightarrow {b})$三向量的终点在一条直线上, 求实数$t$.",
"content": "已知$\\overrightarrow {a}, \\overrightarrow {b}$是两个不共线的向量, 若它们起点相同, $\\overrightarrow {a}$、$\\dfrac{\\overrightarrow {b}}{2}$、$t(\\overrightarrow {a}+\\overrightarrow {b})$三向量的终点在一条直线上, 求实数$t$.",
"objs": [],
"tags": [
"第五单元"
@ -592783,7 +592784,8 @@
],
"origin": "2025届高一下校本作业",
"edit": [
"20230209\t王伟叶"
"20230209\t王伟叶",
"20240224\t王伟叶"
],
"same": [],
"related": [],
@ -592886,7 +592888,7 @@
},
"021775": {
"id": "021775",
"content": "如图, 设$\\overrightarrow {a}=\\overrightarrow{OA}=3 \\overrightarrow{OC}$, $\\overrightarrow {b}=\\overrightarrow{OB}=4 \\overrightarrow{OD}$, 且$\\overrightarrow {a}$、$\\overrightarrow {b}$不共线, $AD$、$BC$交于点$P$, 试用$\\overrightarrow {a}$、$\\overrightarrow {b}$表示$\\overrightarrow{OP}$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (4,1) node [below] {$A$} coordinate (A);\n\\draw (2,3) node [right] {$B$} coordinate (B);\n\\draw ($(O)!{1/3}!(A)$) node [below] {$C$} coordinate (C);\n\\draw ($(O)!{1/4}!(B)$) node [left] {$D$} coordinate (D);\n\\draw (B)--(O)--(A)(B)--(C)(A)--(D);\n\\draw ($(C)!{2/11}!(B)$) node [above right] {$P$} coordinate (P);\n\\draw (O)--(P);\n\\end{tikzpicture}\n\\end{center}",
"content": "如图, 设$\\overrightarrow {a}=\\overrightarrow{OA}=3 \\overrightarrow{OC}$, $\\overrightarrow {b}=\\overrightarrow{OB}=4 \\overrightarrow{OD}$, 且$\\overrightarrow {a}$、$\\overrightarrow {b}$不共线, $AD$、$BC$交于点$P$, 试用$\\overrightarrow {a}$、$\\overrightarrow {b}$表示$\\overrightarrow{OP}$, $\\overrightarrow{QP}=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (4,1) node [below] {$A$} coordinate (A);\n\\draw (2,3) node [right] {$B$} coordinate (B);\n\\draw ($(O)!{1/3}!(A)$) node [below] {$C$} coordinate (C);\n\\draw ($(O)!{1/4}!(B)$) node [left] {$D$} coordinate (D);\n\\draw (B)--(O)--(A)(B)--(C)(A)--(D);\n\\draw ($(C)!{2/11}!(B)$) node [above right] {$P$} coordinate (P);\n\\draw (O)--(P);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [
"第五单元"
@ -592907,7 +592909,8 @@
],
"origin": "2025届高一下校本作业",
"edit": [
"20230209\t王伟叶"
"20230209\t王伟叶",
"20240224\t王伟叶"
],
"same": [],
"related": [],
@ -594308,7 +594311,7 @@
},
"021820": {
"id": "021820",
"content": "如图, $A$、$M$、$B$在同一直线上, 且$\\overrightarrow{AM}=\\dfrac{1}{3} \\overrightarrow{AB}$, 设$\\overrightarrow{OA}=\\overrightarrow {a}$, $\\overrightarrow{OB}=\\overrightarrow {b}$, $\\overrightarrow{OM}=\\overrightarrow {c}$, 用\n$\\overrightarrow {a}$、$\\overrightarrow {b}$表示$\\overrightarrow {c}$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\draw (3,0) node [above] {$B$} coordinate (B);\n\\draw (2,-2) node [below] {$O$} coordinate (O);\n\\draw ($(A)!{1/3}!(B)$) node [above] {$M$} coordinate (M);\n\\draw [->] (A)--(M);\n\\draw [->] (M)--(B);\n\\draw [->] (O)--(M);\n\\draw (O)--(A)(O)--(B);\n\\end{tikzpicture}\n\\end{center}",
"content": "如图, $A$、$M$、$B$在同一直线上, 且$\\overrightarrow{AM}=\\dfrac{1}{3} \\overrightarrow{AB}$, 设$\\overrightarrow{OA}=\\overrightarrow {a}$, $\\overrightarrow{OB}=\\overrightarrow {b}$, $\\overrightarrow{OM}=\\overrightarrow {c}$, 用$\\overrightarrow {a}$、$\\overrightarrow {b}$表示$\\overrightarrow {c}$, $\\overrightarrow{c}=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A);\n\\draw (3,0) node [above] {$B$} coordinate (B);\n\\draw (2,-2) node [below] {$O$} coordinate (O);\n\\draw ($(A)!{1/3}!(B)$) node [above] {$M$} coordinate (M);\n\\draw [->] (A)--(M);\n\\draw [->] (M)--(B);\n\\draw [->] (O)--(M);\n\\draw (O)--(A)(O)--(B);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [
"第五单元"
@ -594329,7 +594332,8 @@
],
"origin": "2025届高一下校本作业",
"edit": [
"20230209\t王伟叶"
"20230209\t王伟叶",
"20240224\t王伟叶"
],
"same": [],
"related": [