Do I need a TV to use a ChromeCast?

I want to use a chromecast straight to my projector (acer x112) unfortunately it doesn't have a HDMI port. I have an Xbox 360 that links to my projector through a VGA however it does not have Xbox Live so I can't receive Iplayer ect. Is there any way of using a ChromeCast without having a TV? For example, could i plug it into my Xbox 360 and stream programmes from my Iphone on to my projector screen through the Xbox without ever coming into contact with a tv?
Cheers

If you don't have a HDMI port, you can't use Chromecast. Period.

If you already havea Xbox 360 connected, then you don't need a Chromecast as the 360 can do everything (and more) the Chromecast can do.