Let $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}$ be the position vectors of the vertices $A, B, C$ respectively of $\triangle A B C$. The vector area of $\triangle A B C$ is :

• A

  $\frac{1}{2}\{\overrightarrow{\mathbf{a}} \times(\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}})+\overrightarrow{\mathbf{b}} \times(\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}})+\overrightarrow{\mathbf{c}} \times(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}})\}$
• Correct answer
  B

  $\frac{1}{2}\{\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}\}$
• C

  $\frac{1}{2}\{\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}\}$
• D

  $\frac{1}{2}\{(\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{c}}) \overrightarrow{\mathbf{a}}+(\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{a}}) \overrightarrow{\mathbf{b}}+(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}) \overrightarrow{\mathbf{c}}\}$

Hence, the correct answer is option: 'B'.