Recently, I worked on a client website where it needed an embed youtube video on the product page. The embedding part wasn’t hard; the hardest part was getting the iFrame to be responsive just like the layout. One of the way that I found which worked quite well is by using the following code:
Hope this helps you when you are embedding video into your website using iFrame and need the iframe to be responsive.
References: http://flwebsites.biz/posts/proportional-responsive-iframes-youtube-videos