Subject: Do 2 intersecting beams of light pick up eachothers color?

Say you're in a room with all white walls, pitch black. Then you turn on 2 spot 
lights, one white and the other red and they intersect eachother. Does the 
white light that intersects the red one, show only white where it hits the 
white wall, or does it have any red in it. I've asked this question to as 
many "smart" people as I could. They've never given an answer they were certain 
of.

Re: Do 2 intersecting beams of light pick up eachothers color?