Here are sentences using each of the given phrases:
Due to : Due to the heavy rain, the outdoor concert was postponed until next week.
In this sentence, "due to" is used to explain the reason for the postponement of the concert, which is the heavy rain.
In the right : After reviewing all the facts, the judge concluded that the defendant was in the right.
Here, "in the right" means that the defendant was correct or justified in their actions as determined by the judge's decision.
In detail : The teacher asked the students to describe their summer vacation in detail.
In this sentence, "in detail" is used to indicate that the teacher expects a thorough and comprehensive description of the students' summer vacation experiences.