If TCP is connection oriented why do packets follow different paths?

Question

According to my knowledge if an internet application has to be designed, we should use either a connection-oriented service or connection-less service, but not both.

Answer 1

router works on three layers only (physical , data link and Network layers) , so routers will take decision depending only on the info. of network layer (IP protocol ) hence there is no information available about its TCP or UDP at the router