The points \[O,\,A,\,B,\,C,\,D\] are such that \[\overrightarrow{OA}=\mathbf{a},\] \[\overrightarrow{OB}=\mathbf{b},\,\] \[\overrightarrow{OC}=2\mathbf{a}+3\mathbf{b}\] and \[\overrightarrow{OD}=\mathbf{a}-2\mathbf{b}.\] If \[|\mathbf{a}|\,=3\,|\mathbf{b}|,\] then the angle between \[\overrightarrow{BD}\] and \[\overrightarrow{AC}\] is

• A. \[\frac{\pi }{3}\]
• B. \[\frac{\pi }{4}\]
• C. \[\frac{\pi }{6}\]
• D. None of these