Here is how to embed videos that are responsive using Vimeo;
Click on the link with your video id in it. For example, go the video you want to embed responsively.
If you can see a download button, just beside it, there is a Share button with a play logo on it.
Click on the Share button with a play logo on it.
A Share this Video windows pops up, and navigate to (click on) "Show options" next to the title "Embed".
A new Share this Video pops up with more options like "Link", "Email" and below the Video itself, there are settings that include a radio button next to "Size" that says "Responsive", click that and copy the code to embed into your HTML divs.