Giải thích các bước giải:
Ta có:
$A=\sqrt{(\vec{AB})^2\cdot (\vec{AC})^2-(\vec{AB}\cdot \vec{AC})^2}$
$\to A=\sqrt{AB^2\cdot AC^2-(AB\cdot AC\cdot \cos\widehat{BAC})^2}$
$\to A=\sqrt{AB^2\cdot AC^2-AB^2\cdot AC^2\cdot \cos^2\widehat{BAC}}$
$\to A=\sqrt{AB^2\cdot AC^2(1- \cos^2\widehat{BAC})}$
$\to A=\sqrt{AB^2\cdot AC^2\cdot \sin^2\widehat{BAC}}$
$\to A=AB\cdot AC\cdot \sin\widehat{BAC}$
Mà $S_{ABC}=\dfrac12AB\cdot AC\cdot \sin\widehat{BAC}$
$\to S=\dfrac12A$
$\to S=\dfrac12\sqrt{(\vec{AB})^2\cdot (\vec{AC})^2-(\vec{AB}\cdot \vec{AC})^2}$
