Vector FE= vector AE- vector AF

Because F.E is the midpoint of AB. AC is,

So vector FE= vector AE- vector AF= 1/2 vector AC- 1/2 vector AB.

= 1/2 (vector AC- vector AB)

= 1/2 vector BC

So vector BC// vector FE,

So BC//FE and FE= 1/2BC.