The statement that correctly analyzes the influence of the Cold War on the Vietnam War is: "A nation’s support for North Vietnam or South Vietnam was determined by its relationship to communism."
During the Cold War, global dynamics were heavily influenced by the ideological struggle between communism and capitalism. North Vietnam received support from communist countries like the Soviet Union and China, while South Vietnam was supported by the United States and other anti-communist nations. This is a clear reflection of the Cold War's impact on the Vietnam War.