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What would be handy first is the manual for the projector.
Then you can find out what the 'PC VGA' is capable of.
You see projectors are like early plasma screens. They have a D-sub 15 pin and they vary in what they're capable of.
Some of them do what is normal for a D-sub. Or should I say standard.
Some of them accept the RGB with composite sync that is actually standard SCART.
And lastly some do both.

Very annoying. It's similar to some progressive DVD players you can get which output component signals through a SCART socket.

You could argue to the cows come home between component and RGB (as in PC RGBHV) But they're about the same. With component in PAL I believe you would get a 576i signal. You could switch video region to NTSC and use 480p. This isn't as bad as it might sound. What I mean is it doesn't affect the games. You have settings for a video region of NTSC and a game region of PAL. Wouldn't it be nice if unmodded consoles came the same way?
If you check the D-sub and it does SCART RGB you'd need a Xbox SCART cable and then another cable connected to it and the projector.
If the D-sub does PC RGBHV (horizontal and vertical sync) you could get 480p with the VGA connection method. You need to convert to NTSC for this as well.

I'd start off with a component cable in PAL and if you want to try 480p look out for the Enigmah switch disc to change from PAL to NTSC. You can burn it to a disc or install it and use it like a .xbe Xbox executable.

If you don't have the manual try googling the projector's make and model number.