Master Details SQL Query

I have two tables , the first table list all the products that are available for sale.
PRODUCT_REGISTRATION
======================
PRODUCT_ID int,
PRODUCT_DESCRIPTION
QUANTITY
....etc

The next table is the Vendor Pricing table where the table holds the price offers from various vendors for a given product.

VENDOR_PRICING
================
ID int
VENDOR_ID int
PRODUCT_ID int
PRICE decimal (18,2)

Now i need to list a view with all the product with the cheapest price.

ie

PRODUCT_REGISTRATION

1,'Samsung LCD',21
2, 'Samsung Camera',250

VENDOR_PRICING

1,1,1,2000
2,1,2,160
3,2, 1,2200
4,3,1,1900

etc

In the above illustation, the Vendor with ID=3  has the cheapest price for the product id=1.

So  i wish to create a view to display the same.

CREATE VIEW dbo.PRODUCT_PRICING_VENDOR_VIEW
AS
SELECT
  VP.ID,
 P.PRODUCT_ID,
 P.PRODUCT_DESCRIPTION,
 P.QUANTITY,
 VP.VENDOR_ID ,
 SELECT MAX(PRICE) FROM VENDOR_PRICING WHERE VP.PRODUCT_ID=P. PRODUCT_ID AS PRICE



WHERE
   VENDOR_PRICING VP LEFT OUTERJOIN
  PRODUCT_REGISTRATION P ON VP.PRODUCT_ID=P. PRODUCT_ID

Can you let me know if this is the method to find the cheapest price.
If not can you change the query to help me get the result i wanted