取 $A$ 為原點，令 $\overset{\large\rightharpoonup}{AB}=\left(2,0,0\right)$、$\overset{\large\rightharpoonup}{AD}=\left(0,3,0\right)$、向下長度為 $5$。則 $\overset{\large\rightharpoonup}{AH}=\left(0,3,5\right)$，$\overset{\large\rightharpoonup}{AC}=\left(2,3,0\right)$，故 $\overset{\large\rightharpoonup}{AH}\cdot\overset{\large\rightharpoonup}{AC}=9$。