Giải thích các bước giải:
$\begin{array}{l}
a)\overrightarrow {AD} + \overrightarrow {BC} \\
= \left( {\overrightarrow {AM} + \overrightarrow {MN} + \overrightarrow {ND} } \right) + \left( {\overrightarrow {BM} + \overrightarrow {MN} + \overrightarrow {NC} } \right)\\
= \left( {\overrightarrow {AM} + \overrightarrow {BM} } \right) + \left( {\overrightarrow {ND} + \overrightarrow {NC} } \right) + 2\overrightarrow {MN} \\
= \overrightarrow 0 + \overrightarrow 0 + 2\overrightarrow {MN} \\
= 2\overrightarrow {MN} \\
b)\overrightarrow {AC} + \overrightarrow {BD} \\
= \left( {\overrightarrow {AM} + \overrightarrow {MN} + \overrightarrow {NC} } \right) + \left( {\overrightarrow {BM} + \overrightarrow {MN} + \overrightarrow {ND} } \right)\\
= \left( {\overrightarrow {AM} + \overrightarrow {BM} } \right) + \left( {\overrightarrow {NC} + \overrightarrow {ND} } \right) + 2\overrightarrow {MN} \\
= \overrightarrow 0 + \overrightarrow 0 + 2\overrightarrow {MN} \\
= 2\overrightarrow {MN}
\end{array}$
