$\left| {\overrightarrow {AC} - \overrightarrow {AB} - \overrightarrow {OC} } \right|$

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

= $\left| {\overrightarrow {BC} + \overrightarrow {CO} } \right|$

= $\left| {\overrightarrow {BO} } \right| = BO$

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