Alright, I guess I'll have a crack at it.
Perpendicular should immediately scream "dot product" at you. Dot product vectors CD and BE which would then equal zero.
So, CD.BE=0, (AD-AC).(AE-AB)=0 -> expand this
Make AD.AE the subject so AD.AE=AB.AD+AC.AE-AC.AB
Since AB || AD, and AC || AE dot...