added sqlite-vec extension

packages/sqlite3_vec/example/lib/main.dart

@@ -0,0 +1,49 @@
+import 'package:flutter/material.dart';
+import 'package:sqlite3/sqlite3.dart';
+import 'package:sqlite3_vec/sqlite3_vec.dart';
+
+void main() async {
+  WidgetsFlutterBinding.ensureInitialized();
+
+  Sqlite3Vec.ensureExtensionLoaded();
+
+  final db = sqlite3.openInMemory();
+
+  runApp(MyApp(db: db));
+}
+
+class MyApp extends StatefulWidget {
+  const MyApp({super.key, required this.db});
+
+  final Database db;
+
+  @override
+  State<MyApp> createState() => _MyAppState();
+}
+
+class _MyAppState extends State<MyApp> {
+  @override
+  void dispose() {
+    widget.db.dispose();
+    super.dispose();
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    final version = widget.db //
+        .select('SELECT vec_version() as version;')
+        .first['version'];
+    return MaterialApp(
+      home: Scaffold(
+        appBar: AppBar(
+          title: const Text('sqlite-vec'),
+        ),
+        body: Center(
+          child: Text(
+            'version: $version',
+          ),
+        ),
+      ),
+    );
+  }
+}