Cho 6 điểm A, B, C, D, E. Chứng minh: −−→ CD + −−→ FA − −−→ BA − −−→ ED + −−→ BC − −→ FE = → 0 .

Lời giải:

Ta có: \(\overrightarrow {{\rm{CD}}} + \overrightarrow {{\rm{FA}}} - \overrightarrow {{\rm{BA}}} - \overrightarrow {{\rm{ED}}} + \overrightarrow {{\rm{BC}}} - \overrightarrow {{\rm{FE}}} \)

\( = \left( {\overrightarrow {{\rm{BC}}} + \overrightarrow {{\rm{CD}}} } \right) + \left( {\overrightarrow {{\rm{FA}}} - \overrightarrow {{\rm{FE}}} } \right) - \overrightarrow {{\rm{BA}}} - \overrightarrow {{\rm{ED}}} \)

\( = \overrightarrow {{\rm{BD}}} + \overrightarrow {{\rm{EA}}} - \overrightarrow {{\rm{BA}}} - \overrightarrow {{\rm{ED}}} \)

\( = \left( {\overrightarrow {{\rm{BD}}} - \overrightarrow {{\rm{BA}}} } \right) + \left( {\overrightarrow {{\rm{EA}}} - \overrightarrow {{\rm{ED}}} } \right)\)

\( = \overrightarrow {{\rm{AD}}} + \overrightarrow {{\rm{DA}}} \)

\( = \overrightarrow 0 \).

Vậy \(\overrightarrow {{\rm{CD}}} + \overrightarrow {{\rm{FA}}} - \overrightarrow {{\rm{BA}}} - \overrightarrow {{\rm{ED}}} + \overrightarrow {{\rm{BC}}} - \overrightarrow {{\rm{FE}}} = \overrightarrow 0 .\)