$${1 \over 2}\left( {\overrightarrow a - \overrightarrow b } \right) \bullet \left( {\overrightarrow a - \overrightarrow c } \right)$$

$${1 \over 2}\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a - \overrightarrow c } \right)} \right|$$

$${1 \over 2}\left| {\overrightarrow a \times \overrightarrow b \times \overrightarrow c } \right|$$

$${1 \over 2}\left( {\overrightarrow a \times \overrightarrow b } \right) \bullet \overrightarrow c $$