Đáp án:
\(x = \frac{1}{5}\)
Giải thích các bước giải:
$\begin{array}{l}
\overrightarrow {BI} = \overrightarrow {BA} + \overrightarrow {AI} = - \overrightarrow {AB} + \frac{1}{2}\overrightarrow {AG} = - \overrightarrow {AB} + \frac{1}{2}.\frac{1}{3}\left( {\overrightarrow {AA} + \overrightarrow {AB} + \overrightarrow {AC} } \right)\\
= - \overrightarrow {AB} + \frac{1}{6}\overrightarrow {AB} + \frac{1}{6}\overrightarrow {AC} = - \frac{5}{6}\overrightarrow {AB} + \frac{1}{6}\overrightarrow {AC} \\
\overrightarrow {BK} = \overrightarrow {BA} + \overrightarrow {AK} = - \overrightarrow {AB} + x\overrightarrow {AC} \\
B,I,K\,thang\,hang \Leftrightarrow \frac{{ - 1}}{{ - \frac{5}{6}}} = \frac{x}{{\frac{1}{6}}} \Leftrightarrow - \frac{1}{6} = - \frac{5}{6}x \Leftrightarrow x = \frac{1}{5}\\
Vay\,x = \frac{1}{5}
\end{array}$
