Final answer:
The principle that guided United States involvement in Vietnam in the 1960s and early 1970s was the Domino Theory, which suggested that the spread of communism in one country would lead to the spread of communism to neighboring countries.
Step-by-step explanation:
The principle that guided United States involvement in Vietnam in the 1960s and early 1970s was the Domino Theory. This theory posited that the spread of communism in one country would lead to the spread of communism to neighboring countries, like falling dominos. The United States believed that if South Vietnam fell to communism, it would pave the way for other countries in Southeast Asia to do the same.