diff --git a/Models/Common.cs b/Models/Common.cs
index 8476bac..f519e2a 100644
--- a/Models/Common.cs
+++ b/Models/Common.cs
@@ -109,6 +109,20 @@ namespace ActiveProtect.Models
             return !(left == right);
         }
 
+        public override bool Equals(object? obj)
+        {
+            if (obj is Vector3D other)
+            {
+                return this == other;
+            }
+            return false;
+        }
+
+        public override int GetHashCode()
+        {
+            return HashCode.Combine(X, Y, Z);
+        }
+
         /// <summary>
         /// 计算向量的模长
         /// </summary>
@@ -190,6 +204,7 @@ namespace ActiveProtect.Models
             Vector3D unitDirection = direction.Normalize();
             return a + unitDirection * distance;
         }
+
     }
 
     /// <summary>