How to make site.ru on one hosting, www.site.ru on another?

Question

Domain Name System

How can I make sure that site.ru is on one hosting, and www.site.ru is on another? At the same time, it is necessary that from site.ru there is a redirect to www.site.ru. The main goal of this action is that when checking in various services, site.ru shows the DNS of site.ru hosting, and not hosting www.site.ru. The idea so far is this, physically the site is located on www.site.ru, and .htaccess with a redirect is located on site.ru

RewriteEngine On
RewriteCond %{HTTP_HOST} ^site.ru$ [NC]
RewriteRule ^(.*)$ http://www.site.ru/$1 [R=301,L]

With regards to domains, I plan to hang www on another hoster through the A-record. Will this work?