The Gulf of Tonkin incident occurred in the Gulf of Tonkin off of the coast of North Vietnam.
The citizens were told the North Vietnamese communists violently attacked a US ship which was peacefully existing to aid South Vietnam. It was presented as a direct threat to the US and a means for war.
The ship was in North Vietnamese territory and was alone away from the rest of the US fleet in South Vietnam. The US was not peaceful as they were attacking the North and supplying the South putting them directly in the war.
Per the Constitution--war is to be asked for by the executive and approved by Congress with an official declaration of war. However, the Gulf of Tonkin Resolution gave permission to Johnson to use war materials and practices without an official declaration of war. This prevented allies from entering the war but allowed the US to engage in war behavior under the executive orders.
Colonies wanted to establish their presence in the New World, Colonies would keep other European countries from trying to claim land and Colonies would keep problems with American Indians in the area to a minimum.
