**Core Concept**
Vitamin K is an essential nutrient that plays a crucial role in the synthesis of clotting factors in the liver. It acts as a cofactor for the enzyme gamma-glutamyl carboxylase, which is responsible for the post-translational modification of certain proteins.

**Why the Correct Answer is Right**
Vitamin K-dependent proteins, such as prothrombin and factors II, VII, IX, and X, require gamma-carboxylation to bind calcium ions and facilitate blood coagulation. This process involves the conversion of glutamate residues to gamma-carboxyglutamate (Gla) residues, which enables these proteins to interact with phospholipid surfaces. The gamma-glutamyl carboxylase enzyme requires vitamin K as a cofactor to perform this modification, highlighting the importance of vitamin K in the coagulation cascade.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because vitamin K is not primarily involved in DNA synthesis or repair. While it does play a role in the synthesis of certain proteins, its function is more closely related to blood coagulation.
**Option B:** This option is incorrect because vitamin K is not directly involved in the regulation of calcium homeostasis. While it does facilitate the binding of calcium ions to vitamin K-dependent proteins, its primary function is not to regulate calcium levels.
**Option C:** This option is incorrect because vitamin K is not a primary antioxidant in the body. While it does have some antioxidant properties, its main function is related to blood coagulation.

**Clinical Pearl / High-Yield Fact**
Vitamin K deficiency can lead to bleeding disorders, including easy bruising and spontaneous bleeding. Patients with malabsorption syndromes, such as celiac disease or Crohn's disease, are at increased risk of vitamin K deficiency.

**Correct Answer: C. Vitamin K is essential for the synthesis of clotting factors in the liver.**