**Core Concept**
The question is testing the student's knowledge of the anatomical relationships between the left vagus nerve and the left phrenic nerve at the level of the arch of the aorta. This knowledge is crucial for understanding the thoracic anatomy and the pathways of various nerves in the mediastinum.

**Why the Correct Answer is Right**
At the level of the arch of the aorta, the left phrenic nerve lies anterior to the left vagus nerve. This is because the phrenic nerve descends from the neck through the thoracic cavity, passing anterior to the subclavian artery and the vagus nerve. As it reaches the level of the arch of the aorta, it crosses over the vagus nerve, which lies in a more posterior position. The left vagus nerve then continues to descend through the thoracic cavity, giving off branches to the heart and lungs.

**Why Each Wrong Option is Incorrect**
**Option B:** The phrenic nerve is not posterior to the vagus nerve at this level, as this would be an incorrect anatomical relationship.
**Option C:** The phrenic and vagus nerves do not lie in the same plane anteroposteriorly at the level of the arch of the aorta, as the phrenic nerve is anterior and the vagus nerve is posterior.
**Option D:** While anatomical relationships can be variable in some cases, the relationship between the left phrenic and vagus nerves at the level of the arch of the aorta is generally consistent and not variable.

**Clinical Pearl / High-Yield Fact**
It's essential to remember the anatomical relationships between various nerves in the thoracic cavity, as knowledge of these relationships can be critical for diagnosing and treating conditions such as thoracic outlet syndrome, phrenic nerve palsy, and vagal nerve stimulation.

**✓ Correct Answer: A. Phrenic nerve anterior, vagus nerve posterior**