收录高三寒假作业30新题

工具v2/文本文件/新题收录列表.txt

@@ -88,3 +88,6 @@
 20240125-113548
 023848:023855
 
+20240125-113926
+023856:023864
+

题库0.3/Problems.json

@@ -26143,7 +26143,9 @@
             "20220624\t朱敏慧, 王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023858"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -61720,7 +61722,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023860"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -67389,7 +67393,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023862"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -69886,7 +69892,9 @@
             "20220625\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023857"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -247624,7 +247632,9 @@
             "20220726\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023857"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -398989,7 +398999,9 @@
             "20230202\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023856"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -643640,6 +643652,198 @@
         "space": "4em",
         "unrelated": []
     },
+    "023856": {
+        "id": "023856",
+        "content": "设向量 $\\overrightarrow{a}=(3,2)$, $\\overrightarrow{b}=(1,-4)$, 则 $\\overrightarrow{b}$ 在 $\\overrightarrow{a}$ 方向上的数量投影为\\blank{50}, 投影为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "014337"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023857": {
+        "id": "023857",
+        "content": "已知点 $A(8,-1)$、$B(1,-3)$, 若点 $C(2 m-1, m+2)$ 在直线 $AB$ 上, 则实数 $m=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "008761",
+            "002149"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023858": {
+        "id": "023858",
+        "content": "设向量 $\\overrightarrow{p}=(2,7)$, $\\overrightarrow{q}=(x,-3)$. 若 $\\overrightarrow{p}$ 与 $\\overrightarrow{q}$ 的夹角为钝角, 则 $x$ 的取值范围是\\blank{50}, 若 $\\overrightarrow{p}$ 与 $\\overrightarrow{q}$ 的夹角为锐角, 则 $x$ 的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "000699",
+            "040747"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023859": {
+        "id": "023859",
+        "content": "已知 $|\\overrightarrow{a}|=5$, $|\\overrightarrow{b}|=8, \\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 的夹角为 $60^{\\circ}$, 则 $|\\overrightarrow{a}+\\overrightarrow{b}|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023860": {
+        "id": "023860",
+        "content": "设 $\\overrightarrow{a}=(m+1,-3)$, $\\overrightarrow{b}=(1, m-1)$, 且 $\\overrightarrow{a}+\\overrightarrow{b}$ 与 $\\overrightarrow{a}-\\overrightarrow{b}$ 垂直, 则实数 $m=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "001891"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023861": {
+        "id": "023861",
+        "content": "若 $|\\overrightarrow{a}|=3$, $|\\overrightarrow{b}|=4$, $(\\overrightarrow{a}+2 \\overrightarrow{b}) \\cdot(2 \\overrightarrow{a}-\\overrightarrow{b})=-32$, 则 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 的夹角为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023862": {
+        "id": "023862",
+        "content": "若将向量 $\\overrightarrow{a}=(3,4)$ 绕原点按逆时针方向旋转 $45^{\\circ}$ 得到向量 $\\overrightarrow{b}$, 则 $\\overrightarrow{b}$ 的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "002062"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023863": {
+        "id": "023863",
+        "content": "已知 $O$ 为坐标原点, $\\overrightarrow{OA}=(2,2)$, $\\overrightarrow{OB}=(4,1)$, 点 $P$ 在 $x$ 轴上, 则 $\\overrightarrow{AP}\\cdot \\overrightarrow{BP}$ 最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023864": {
+        "id": "023864",
+        "content": "在平面直角坐标系 $x O y$ 中, 点 $A(-1,-2)$、$B(2,3)$、$C(-2,-1)$.\\\\\n(1) 求以线段 $AB$、$AC$ 为邻边的平行四边形两条对角线的长;\\\\\n(2) 设实数 $t$ 满足 $(\\overrightarrow{AB}-t \\overrightarrow{OC}) \\cdot \\overrightarrow{OC}=0$, 求实数 $t$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "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.",
@@ -718479,7 +718683,9 @@
             "20230516\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023858"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []