$\begin{array}{l}
\overrightarrow {AM} + 2\overrightarrow {MB} = \overrightarrow 0 \Leftrightarrow \overrightarrow {AM} + 2\left( {\overrightarrow {AB} - \overrightarrow {AM} } \right) = \overrightarrow 0 \\
\Leftrightarrow - \overrightarrow {AM} + 2\overrightarrow {AB} = \overrightarrow 0 \Leftrightarrow \overrightarrow {AM} = 2\overrightarrow {AB} \\
\overrightarrow {MN} = \overrightarrow {AN} - \overrightarrow {AM} = 2\overrightarrow {AC} - 2\overrightarrow {AB} \\
= 2\left( {\overrightarrow {AC} - \overrightarrow {AB} } \right) = 2\overrightarrow {BC} \\
\overrightarrow {AD} + \overrightarrow {PD} = \overrightarrow 0 \Leftrightarrow \overrightarrow {PD} = - \overrightarrow {AD} \Leftrightarrow \overrightarrow {AD} - \overrightarrow {AP} = - \overrightarrow {AD} \\
\Leftrightarrow \overrightarrow {AP} = 2\overrightarrow {AD} \\
\overrightarrow {NP} = \overrightarrow {AP} - \overrightarrow {AN} = 2\overrightarrow {AD} - 2\overrightarrow {AC} = 2\left( {\overrightarrow {AD} - \overrightarrow {AC} } \right) = 2\overrightarrow {CD}
\end{array}$
b) M,N,P thẳng hàng
$ \Leftrightarrow \overrightarrow {MN} = k\overrightarrow {NP} \Leftrightarrow 2\overrightarrow {BC} = 2k\overrightarrow {CD} \Leftrightarrow \overrightarrow {BC} = k\overrightarrow {CD} $
hay B,C,D thẳng hàng.
