Area = \(\frac{1}{2}|\vec{AB} \times \vec{AC}| = \frac{1}{2}|(\vec{b} - \vec{a}) \times (\vec{c} - \vec{a})|\)

Expanding: \((\vec{b} - \vec{a}) \times (\vec{c} - \vec{a}) = \vec{b} \times \vec{c} - \vec{b} \times \vec{a} - \vec{a} \times \vec{c} = \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}\)

Area = \(\frac{1}{2}|\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}|\)

Answer: (A)