diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 3c11d779..393a523d 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -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": [],