$\vec{AB}$.$\vec{AD}$ = |$\vec{AB}$|. |$\vec{AD}$|. cos($\vec{AB}$, $\vec{AD}$) = a. a. $cos90^{\circ}$ = 0
$\vec{AB}$.$\vec{AC}$ = |$\vec{AB}$|. |$\vec{AC}$|. cos($\vec{AB}$, $\vec{AC}$) = a.$\sqrt{2}$a.$cos45^{\circ}$ = $a^{2}$
$\vec{AC}$. $\vec{CB}$ = |$\vec{AC}$|. |$\vec{CB}$|. cos($\vec{AC}$, $\vec{CB}$) = $\sqrt{2}$a. a. $cos135^{\circ}$ = $-a^{2}$
$\vec{AC}$. $\vec{BD}$ = |$\vec{AC}$|. |$\vec{BD}$|. cos($\vec{AC}$, $\vec{BD}$) = $\sqrt{2}$a. $\sqrt{2}$a. $cos90^{\circ}$ = 0