Đáp án:
\( \Rightarrow \overrightarrow {MC} = 6\overrightarrow {AK} + 4\overrightarrow {AM} \)
Giải thích các bước giải:
\(\begin{array}{l}\overrightarrow {MC} = \overrightarrow {MA} + \overrightarrow {AC} = - \dfrac{1}{2}\overrightarrow {AB} + \overrightarrow {AC} \\\overrightarrow {AK} = \dfrac{1}{2}\left( {\overrightarrow {AM} + \overrightarrow {AN} } \right) = \dfrac{1}{2}.\left( {\dfrac{1}{2}\overrightarrow {AB} + \dfrac{1}{3}\overrightarrow {AC} } \right) = \dfrac{1}{4}\overrightarrow {AB} + \dfrac{1}{6}\overrightarrow {AC} \\\overrightarrow {AM} = - \dfrac{1}{2}\overrightarrow {AB} \end{array}\)
Đặt \(\overrightarrow {MC} = k\overrightarrow {AK} + l\overrightarrow {AM} \) thì \(\left\{ \begin{array}{l} - \dfrac{1}{2} = \dfrac{1}{4}k - \dfrac{1}{2}l\\1 = \dfrac{1}{6}k\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}k = 6\\l = 4\end{array} \right.\)
\( \Rightarrow \overrightarrow {MC} = 6\overrightarrow {AK} + 4\overrightarrow {AM} \)
