Describe the relationship between Europeans, Native Americans, and Africans in the 1600s.
This is a large, multi-faceted question, which changes depending on where in the world the encounters are taking place, which sub-groups of each type are coming into our focus, and even what levels of the respective societies are relating. That said, if we focus on the Americas, in general the encounter of these three groups was characterized by increased dominance and power of Europeans, a decrease in territorial holdings and power for Native Americans, and the ramping up of the African slave trade—first to the Caribbean's highly profitable sugar plantations and then to the mainland of North and South America to work in the various plantations that began to proliferate in those places.
The power imbalance was in large part due to European technological dominance, especially gun-powder, weaponry, and navigation. There is evidence and speculation that even before the Europeans arrived in parts of the Americas, their diseases, which the indigenous people had little immunity to, took a devastating toll upon their populations, potentially killing millions.
In some parts of North America, there was cooperation, and strategic alliances were made between the tribes and the various European powers. Ultimately, the trend was for these treaties and alliances to be broken by the Europeans whenever they wished to control more land and resources.
Religion added another flavor to the mix. Some Europeans, namely the Catholic Spanish and the Portuguese, viewed the religious conversion of the natives to be part of a broader civilizing mission. The protestant Dutch and English were less concerned with religious conversion and more bent on securing territory for their populations to settle, while the early French explorers to Canada actually had the problematic tendency (from the point of view of the French ruling class) of integrating into the culture of the indigenous inhabitants.
Between 1525 and 1866, 12.5 million slaves were loaded on ships to the new world. Of those, 10.7 million survived the passage. Of those, only 388,000 were shipped directly to North America—the majority were sent to the more profitable sugar plantations of the Caribbean and South America.
The relationship between Europeans, Africans and Indians was one that was dominated by Europeans. The primary reason for this dominance, of course, was the use of guns and superior weapons. Europeans also had the notion that their race was superior to African and Native races. They even used religion to justify their actions. In the New World, Europeans had already begun to settle by the 1600's. The Seventeenth Century was an important period for colonization in North America by Europeans. In 1629, the Puritans began arriving in New England. Their relationship with the Indians was one of cooperation, but it was also violent at times. Over time, the European populations that settled in America would remove Native Americans from their lands. This was done through unfair treaties, but most often by force. European diseases also ravaged the native populations.
The Seventeenth Century also marked an escalation of the European exploitation of Africans. The century saw the development of a large-scale trade network in which very few Africans benefited economically or politically. In 1619, the first slaves were brought to the territory that would become the United States. Millions of African slaves would be captured in Africa and brought to North America. Millions would die in the voyage. This dominant relationship was also based on superior weapons that the Europeans possessed. In the 1600's, Europeans like the Portuguese, Dutch, English and French perpetrated crimes against Indians and Africans that these groups would never recover from.