Two sides of the triangle are \(\vec{AB} = \vec{b} - \vec{a}\) and \(\vec{AC} = \vec{c} - \vec{a}\).

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

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

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

Answer: (B)