In this question, we are asked to find the option that is opposite in meaning to the underlined word "vehement."
The word "vehement" is an adjective that means intense, forceful, or passionate. To find the opposite of this, we need to look for an option that represents the opposite qualities.
Option 1: "animated" means lively or full of energy. This is not the opposite of "vehement" as both words convey a sense of intensity or passion.
Option 2: "apathetic" is the correct answer. It means showing a lack of interest, enthusiasm, or concern. This is the opposite of the intense and passionate nature represented by "vehement."
Option 3: "fervent" means having or showing great intensity or feeling. This is similar in meaning to "vehement" and not opposite.
Option 4: "vigorous" means strong, energetic, or forceful. Like the word "vehement," it conveys a sense of intensity and passion, so it is not the opposite.
Therefore, the correct answer is option 2, "apathetic."