Đáp án:
$\dfrac{{12}}{5}$
Giải thích các bước giải:
$\begin{array}{l}
BC = \sqrt {A{B^2} + A{C^2}} = \sqrt {{6^2} + {8^2}} = 10\\
\Rightarrow BK = \dfrac{2}{5}BC \Rightarrow \overrightarrow {BK} = \dfrac{2}{5}\overrightarrow {BC} \\
\overrightarrow {AK} = \overrightarrow {AB} + \overrightarrow {BK} = \overrightarrow {AB} + \dfrac{2}{5}\overrightarrow {BC} = \overrightarrow {AB} + \dfrac{2}{5}\left( {\overrightarrow {AC} - \overrightarrow {AB} } \right)\\
= \overrightarrow {AB} + \dfrac{2}{5}\overrightarrow {AC} - \dfrac{2}{5}\overrightarrow {AB} = \dfrac{3}{5}\overrightarrow {AB} + \dfrac{2}{5}\overrightarrow {AC} \\
\Rightarrow \left\{ \begin{array}{l}
m = \dfrac{3}{5}\\
n = \dfrac{2}{5}
\end{array} \right. \Rightarrow S = 2.\dfrac{3}{5} + 3.\dfrac{2}{5} = \dfrac{{12}}{5}
\end{array}$
