Embed existing document into newly created document

[dariel87]

• Laravel-mongodb Version: 8.34.0
• PHP Version: 8.0
• Database Driver & Version: 3.8

I have 2 models, Product and Vendor. when I want to create a new product, I need to embed existing vendor to my new product. so far, this is what I have done:

$vendor = Vendor::find($request->vendor);
$product = Product::create([
    'name'=>$request->name
    'vendor'=>$vendor
]);

that code resulting the following document

{
    "_id": "606ffac287be2020b968c613",
    "name": "product name",
    "vendor": {
        "incrementing": true,
        "exists": true,
        "wasRecentlyCreated": false,
        "timestamps": true
    },
    "updated_at": "2021-04-09T06:57:06.032000Z",
    "created_at": "2021-04-09T06:57:06.032000Z"
},

so, what is the correct way to embed existing document into newly created document?
PS: I also tried to save the vendor just like the documentation said, that is:

$product->vendor()->save($vendor)