assassinator2.0,
What you could have seen were Dassault Falcon 50 (http://en.wikipedia.org/wiki/Dassault_Falcon_50), 900 (http://en.wikipedia.org/wiki/Dassault_Falcon_900), or 7X (http://en.wikipedia.org/wiki/Falcon_7X) private jets. They are tri-jets so they comply with your description of having 3 engines on the tail. The purple paint may have been the business jet's owner(s) decision as it is after all their plane.
However, the tail is more of a lower case 't' tail rather than a 'T' tail.
This is the Dassault Falcon 7X. You can see the undercarriage from this angle.
This is the Dassault Falcon 50. The tail shape and 2 of the 3 engines are clearly visible. I'm guessing that you can imagine where the 3rd one would be.
(Pictures courtesy of Wikimedia.)