Difficult
Let $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ be the position vectors of the vertices $A, B, C$ respectively of $\triangle ABC$. The vector area of $\triangle ABC$ is:
- A$\frac{1}{2}\{\overrightarrow{a} \times(\overrightarrow{b} \times \overrightarrow{c})+\overrightarrow{b} \times(\overrightarrow{c} \times \overrightarrow{a})+\overrightarrow{c} \times(\overrightarrow{a} \times \overrightarrow{b})\}$
- B$\frac{1}{2}\{\overrightarrow{a} \times \overrightarrow{b}+\overrightarrow{b} \times \overrightarrow{c}+\overrightarrow{c} \times \overrightarrow{a}\}$
- C$\frac{1}{2}\{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\}$
- D$\frac{1}{2}\{(\overrightarrow{b} \cdot \overrightarrow{c}) \overrightarrow{a}+(\overrightarrow{c} \cdot \overrightarrow{a}) \overrightarrow{b}+(\overrightarrow{a} \cdot \overrightarrow{b}) \overrightarrow{c}\}$
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