Giải thích các bước giải:
\(\begin{array}{l}
a,\\
\overrightarrow {MN} = \overrightarrow {MA} + \overrightarrow {AD} + \overrightarrow {DN} \\
= \frac{1}{2}\overrightarrow {BA} + \overrightarrow {AD} + \frac{1}{2}\overrightarrow {DC} \\
= \frac{1}{2}\left( {\overrightarrow {BC} + \overrightarrow {CD} + \overrightarrow {DA} } \right) + \overrightarrow {AD} + \frac{1}{2}\overrightarrow {DC} \\
= \frac{1}{2}\left( {\overrightarrow {BC} + \overrightarrow {DA} } \right) + \frac{1}{2}\left( {\overrightarrow {CD} + \overrightarrow {DC} } \right) + \overrightarrow {AD} \\
= \frac{1}{2}\left( {\overrightarrow {BC} - \overrightarrow {AD} } \right) + \frac{1}{2}\overrightarrow 0 + \overrightarrow {AD} \\
= \frac{1}{2}\left( {\overrightarrow {AD} + \overrightarrow {BC} } \right)\\
b,\\
\overrightarrow {MN} = \overrightarrow {MA} + \overrightarrow {AC} + \overrightarrow {CN} \\
= \frac{1}{2}\overrightarrow {BA} + \overrightarrow {AC} + \frac{1}{2}\overrightarrow {CD} \\
= \frac{1}{2}\left( {\overrightarrow {BD} + \overrightarrow {DC} + \overrightarrow {CA} } \right) + \overrightarrow {AC} + \frac{1}{2}\overrightarrow {CD} \\
= \frac{1}{2}\left( {\overrightarrow {BD} + \overrightarrow {CA} } \right) + \frac{1}{2}\left( {\overrightarrow {DC} + \overrightarrow {CD} } \right) + \overrightarrow {AC} \\
= \frac{1}{2}\left( {\overrightarrow {BD} - \overrightarrow {AC} } \right) + \frac{1}{2}\overrightarrow 0 + \overrightarrow {AC} \\
= \frac{1}{2}\left( {\overrightarrow {BD} + \overrightarrow {AC} } \right)
\end{array}\)
