a) $\overrightarrow {BA} \,.\,\overrightarrow {BC} $ or $\overrightarrow {AB} \,.\,\overrightarrow {CB} $

$\overrightarrow {BA}  = \left( \begin{gathered}
   - 2 \hfill \\
  \,\,1 \hfill \\
  \,\,2 \hfill \\ 
\end{gathered}  \right)$,  $\overrightarrow {BC}  = \left( \begin{gathered}
  \,\,6 \hfill \\
   - 2 \hfill \\
  \,\,3 \hfill \\ 
\end{gathered}  \right)$

$\overrightarrow {BA} \,.\,\overrightarrow {BC}  =  - 8$

$ = 3 \times 7 \times \cos \theta $

$ \to \theta  = {112.4^ \circ }$ or $1.96$ radians

b) $\overrightarrow {OD}  = \overrightarrow {OA}  + \overrightarrow {AD}  = \overrightarrow {OA}  + \overrightarrow {BC} $

$ = \left( \begin{gathered}
  8 \hfill \\
  1 \hfill \\
  8 \hfill \\ 
\end{gathered}  \right)$