\(\left\{{}\begin{matrix}\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{AD}\\\overrightarrow{BD}=\overrightarrow{BA}+\overrightarrow{AD}=-\overrightarrow{AB}+\overrightarrow{AD}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AB}=\frac{\overrightarrow{AC}-\overrightarrow{BD}}{2}\\\overrightarrow{AD}=\frac{\overrightarrow{AC}+\overrightarrow{BD}}{2}\end{matrix}\right.\)
\(\Rightarrow\overrightarrow{AB}.\overrightarrow{AD}=\left(\frac{\overrightarrow{AC}-\overrightarrow{BD}}{2}\right)\left(\frac{\overrightarrow{AC}+\overrightarrow{BD}}{2}\right)=\frac{\overrightarrow{AC}^2-\overrightarrow{BD}^2}{4}=\frac{3^2-7^2}{4}=-10\)
