how to make a video fill the whole responsive container / browser window?

I would like to make the video fill the whole window (or container) by zooming in when needed so there is no letterbox..

My problem is it only works with the width of the video. Any help would be appreciated.

This is the code i am using:

var vid = sym.$("vid_1_holder");

vid.html('<video width="100%" height = "auto" src = "video/1.mp4" type = "video/mp4" autoplay = "autoplay" loop = "loop"></video>');

Thanks in advance