Lời giải

a) \(\overrightarrow {AB} + \overrightarrow {CD} = \overrightarrow {AD} + \overrightarrow {DB} + \overrightarrow {AD} + \overrightarrow {CB} + \overrightarrow {BD} = \overrightarrow {AD} + \overrightarrow {CB} \)

b) • \(\overrightarrow {AM} + \overrightarrow {BN} + \overrightarrow {CE} = \overrightarrow {AN} + \overrightarrow {NM} + \overrightarrow {BE} + \overrightarrow {CM} + \overrightarrow {CM} + \overrightarrow {ME} \)

\( = \left( {\overrightarrow {AN} + \overrightarrow {BE} + \overrightarrow {CM} } \right) + \left( {\overrightarrow {CM} + \overrightarrow {NM} + \overrightarrow {ME} } \right)\)

\( = \left( {\overrightarrow {AN} + \overrightarrow {BE} + \overrightarrow {CM} } \right) + \overrightarrow {EE} = \left( {\overrightarrow {AN} + \overrightarrow {BE} + \overrightarrow {CM} } \right) + \overrightarrow 0 \)

\( = \overrightarrow {AN} + \overrightarrow {BE} + \overrightarrow {CM} \)

• \(\overrightarrow {AM} + \overrightarrow {BN} + \overrightarrow {CE} = \overrightarrow {AE} + \overrightarrow {EM} + \overrightarrow {BM} + \overrightarrow {MN} + \overrightarrow {CN} + \overrightarrow {NE} \)

\( = \left( {\overrightarrow {AE} + \overrightarrow {BM} + \overrightarrow {CN} } \right) + \left( {\overrightarrow {EM} + \overrightarrow {MN} + \overrightarrow {NE} } \right)\)

\( = \left( {\overrightarrow {AE} + \overrightarrow {BM} + \overrightarrow {CN} } \right) + \overrightarrow {EE} = \left( {\overrightarrow {AE} + \overrightarrow {BM} + \overrightarrow {CN} } \right) + \overrightarrow 0 \)

\( = \overrightarrow {AE} + \overrightarrow {BM} + \overrightarrow {CN} \).

Vậy \(\overrightarrow {AM} + \overrightarrow {BN} + \overrightarrow {CE} = \overrightarrow {AN} + \overrightarrow {BE} + \overrightarrow {CM} = \overrightarrow {AE} + \overrightarrow {BM} + \overrightarrow {CN} \).