In the process of exploration, was da Gama's use of violence justified?
The original question had to be edited. da Gama's voyages had been commissioned for exploration and economic gain. Certainly, da Gama's sincere belief in carrying out the will of the Portuguese Royalty is what inspired his exploration and exploitation. Like many explorers of the time period, da Gama interpreted indigenous people as forces to be overcome and exploited. He recognized clearly that the Hindu and Muslim leaders and indigenous peoples in India might not have received him in the most welcoming fashion. This recognition, coupled with the fact that his stated purpose in exploring was for "Christianity and spices," inspired him with a zeal that compelled him and caused him to believe that, in his exploration, his use of violence was justified.
One of the challenges in assessing questions of exploration is that the use of violence in the time period was viewed fundamentally differently from how it is viewed currently. Violence in the commission of exploration was seen as part of the process. Boats encountered rival vessels, conflict emerged and violence resulted. It was justified under the conditions of naval exploration.
With that being said, I think that one has to seriously assess some of the violence and cruelty that da Gama perpetrated under the zeal of exploration. His encounter with a boat of Muslim pilgrims, with women and children, that led him to burn the boat with all of the people in it is fairly savage. The task of "consolidating" Portuguese control of the seas was something that da Gama took to with passion resulting in his committing some of horrible maritime atrocities. The burning of women and children who were begging for mercy is a display of violence that has to be examined carefully. While understanding that the time period embraced violence, it should not operate as a free pass for explorers like da Gama to escape moral responsibility for what was done in the name of exploration.