What was the u. s. involvement in the vietnam war and soviet union's involvement in afghanistan were motivated mainly by.

Our involvement in vietnam was motivated by trying to reduce the influence of communist power in Asia. It was thought that if Vietnam was lost to communist control, other countries in the region like Korea, Japan and the Philippines would fall into communist control (among others) and countries like Russia and China could find themselves with striking ability to US forces in the Pacific Ocean. They would also have industrial benefits from the natural resources and people in those countries if they fell to communist control which was something that the US found to be against their security interests. 

As far as the Soviet Union and Afghanistan, I'm not entirely sure what their motivation was for that effort. I speculate that having control of Afghanistan would reap some natural resources and territory, but it would have also given them more leverage in world affairs concerning the middle east, where the US and Israel and their allies were controlling the politics in the region mostly. It would have made them much more powerful in world affairs if they did in fact end up controlling Afghanistan, because they could have backed anti-Israeli and US interests by providing military and intelligence support to countries like Syria,Lebanon, and Iran who have not really welcomed or supported Israel as a nation, nor their support from the US and other countries. This would have given them leverage when dealing with the US in global politics, because to avoid actual war, we may have had to make concessions to keep our allies and interests in the region in order. That all however, is speculation on my part but it does make a whole lot of sense understanding the state of global politics at the time.