令 $T=(\overset{\large\rightharpoonup}{AB}\times\overset{\large\rightharpoonup}{AD})\cdot\overset{\large\rightharpoonup}{AP}$。由 $$(\overset{\large\rightharpoonup}{AD}\times\overset{\large\rightharpoonup}{AP})\times(\overset{\large\rightharpoonup}{AP}\times\overset{\large\rightharpoonup}{AB})=T\overset{\large\rightharpoonup}{AP}$$ 左側為 $(-2,0,-4)\times(6,-10,-8)=(-40,-40,20)$，長度為 $60$，且 $AP=6$，故 $|T|=10$。取相容方向可得 $\overset{\large\rightharpoonup}{AB}=(-1,1,-2)$，$\overset{\large\rightharpoonup}{AD}=(-2,-3,1)$，$\overset{\large\rightharpoonup}{AP}=(-4,-4,2)$。逐一檢查頂點，最長為 $\overset{\large\rightharpoonup}{AD}+\overset{\large\rightharpoonup}{AP}=(-6,-7,3)$，距離 $$\sqrt{36+49+9}=\sqrt{94}$$