Our Proto-Indo-European root is *h₃reǵ- "to move in a straight line". The suffixed zero-grade form *h₃r̥ǵ-yo- became Sanskrit ऋज्यति r̥jyati "to stretch out, strive after, long for", then राजी rājī and राजिका rājikā "streak, line, black mustard". This last combined with तिक्तक tiktaka "bitter" (from तेजते tejate "to be sharp" from PIE *steig- "to stick, pointed") to form *rājikātiktaka- "mustard pickle", which became Hindi रायता rāyatā and English raita.
Unfortunately I don't know the details of how the awesome word *rājikātiktaka- was contracted to rāyatā, but this derivation is given in both the AHD and the Oxford Hindi-English dictionary.
In Greek *h₃reǵ- became ὀρέγω oregō "to reach out, to reach after, grasp for", then orexis "appetite" - the "reach after" sense being extended metaphorically to "appetite". This plus the negative prefix an- formed anorexiā "without appetite".
The suffixed form *h₃reǵ-to- became Proto-Germanic *reχtaz, Old English riht "right, correct, straight", and English right.