**Core Concept**
The patient's loss of position and vibration sense from the lower half of the body suggests a lesion affecting the posterior (dorsal) columns of the spinal cord. This is due to the involvement of the fasciculus gracilis and fasciculus cuneatus, which are responsible for transmitting proprioception and vibration sense.

**Why the Correct Answer is Right**
The fasciculus gracilis and fasciculus cuneatus are part of the posterior columns of the spinal cord, which transmit sensory information from the body to the brain. The fasciculus gracilis carries information from the lower body, while the fasciculus cuneatus carries information from the upper body. Damage to these pathways results in the loss of position and vibration sense, making option **C**, the posterior columns of the spinal cord, the correct answer. This is due to the involvement of the medial lemniscus, a pathway that carries proprioceptive and vibratory information from the body to the brain.

**Why Each Wrong Option is Incorrect**
* **Option A:** The corticospinal tract is responsible for motor function, not sensory function.
* **Option B:** The spinothalamic tract is responsible for transmitting pain and temperature sensations, not position or vibration sense.
* **Option D:** The dorsal root ganglia are involved in transmitting sensory information from the body to the spinal cord, but not from the spinal cord to the brain.

**Clinical Pearl / High-Yield Fact**
The loss of position and vibration sense is known as astereognosis, which means the inability to identify objects by touch. This is a classic sign of a lesion in the posterior columns of the spinal cord.

**Correct Answer:** C. The posterior columns of the spinal cord.