Select the correct active form of the given sentence:

Why was such a letter written by your brother?

Why did your brother write such a letter?

The correct answer is Option (2) → Why did your brother write such a letter?

The reason for selecting option (2) as the correct active form of the given sentence is that it follows the standard structure for forming questions in the past tense in English. In this structure, "did" is used as an auxiliary verb to form the question, and the main verb "write" remains in its base form. This results in the correct active question form:

"Why did your brother write such a letter?"