Why did the colonists believe that king george was trying to have them killed?

In the later part of his life, George III had recurrent, and eventually permanent, mental illness. Thus thinking that King George was mad, they believed that he was trying to have them killed

president thomas jefferson commissioned the expedition shortly after the louisiana purchase in 1803 to explore and to map the newly acquired territory, to find a practical route across the western half of the continent, and to establish an american presence in this territory before britain and other european powers