I ordered a longer component cable for my 360 so I can finally hook it up to my projector in my theater room. Question I have is how am I going to connect this new cable to the 360???

i cant post links but search " rgb coupler" on monoprice

Link. :)
http://www.monoprice.com/products/product.asp?c_id=104&cp_id=10401&cs_id=1040107&p_id=3002&seq=1&format=2&style=

You can use the thing tokerblue showed or just get 3 female to female RCA adapters from a electronics store.