How we cite our quotes: (Paragraph)
Quote #1
[…] naval units of the Communist regime in Vietnam, in violation of the principles of the Charter of the United Nations and of international law, have deliberately and repeatedly attacked United States naval vessels lawfully present in international waters, and have thereby created a serious threat to international peace […] (2)
Congress puts Vietnam's attack front and center here. By pointing out that aggression, they are justifying military action in response. Notice the finger-pointing: the document is calling Vietnam out for violating international law, and attacking ships that were legally stationed. By using phrases like "threat to international peace" the U.S. is making Vietnam look like the bad guys of the world, which adds to the justification for action against them.
Quote #2
Whereas these attackers are part of a deliberate and systematic campaign of aggression that the Communist regime in North Vietnam has been waging against its neighbors […] (3)
The idea of revenge extends beyond just U.S. ships. By stating that North Vietnam is attacking other countries in the region (which may or may not have been true), the U.S. is giving itself justification (in the eyes of the world) for intervening. As in, since America is a big, strong country they can go in and defend all the small, weak countries who are being attacked. The key is that the U.S. and these other countries were (allegedly) attacked first, which makes a military response much easier to accept.
Quote #3
[…] the Congress approves and supports the determination of the President, as Commander in Chief, to take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression. (5)
Now this is some careful wording by Congress. They say that America is going to use armed force to fight back against attacks that targeted the U.S. They mean that the floodgates are now open for the U.S. to wage war in Vietnam for whatever ends America might desire. In this case, the hidden agenda (or not so hidden) is to combat the spread of communism. The idea of attacking out of revenge, or protecting others, is simply a convenient excuse in order to not look like the bad guys.