\(\left| {\overrightarrow {AC} - \overrightarrow {AB} - \overrightarrow {OC} } \right|\)

= \(\left| {\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {AB} + \overrightarrow {CO} } \right|\)

= \(\left| {\overrightarrow {BC} + \overrightarrow {CO} } \right|\)

= \(\left| {\overrightarrow {BO} } \right| = BO\)

Gọi M là trung điểm AC

Suy ra: BO = \(\frac{2}{3}BM\)

\(BM = \sqrt {A{B^2} - A{M^2}} = \sqrt {{a^2} - {{\left( {\frac{a}{2}} \right)}^2}} = \frac{{a\sqrt 3 }}{2}\)

BO = \(\frac{{a\sqrt 3 }}{2}.\frac{2}{3} = \frac{{a\sqrt 3 }}{3}\)

Vậy \(\left| {\overrightarrow {AC} - \overrightarrow {AB} - \overrightarrow {OC} } \right| = \frac{{a\sqrt 3 }}{3}\).