Middle English word rek comes from Proto-Indo-European *rowgi-, Proto-Indo-European *rewe-, and later Proto-Germanic *raukiz (Smoke, vapour.)

Detailed word origin of rek

Dictionary entry	Language	Definition
*rowgi-	Proto-Indo-European (ine-pro)
*rewe-	Proto-Indo-European (ine-pro)
*rewg-	Proto-Indo-European (ine-pro)
*raukiz	Proto-Germanic (gem-pro)	Smoke, vapour.
rīec	Scots (sco)
rec	Old English (ang)	Smoke.
rīec	Old English (ang)
reke	Middle English (enm)

Words with the same origin as rek