Hi Dimitris! Are you talking about a noun or a verb? First, 「向かう（muka-u)」is a verb meaning “to head for” or “to face”. 「向かい（mukai)」is a noun derived from the verb meaning “facing”, “opposite” or “other side”” You are confused about okurigana, kana suffixes following kanji stems. 「向い(mukai)」and「向かい (mukai)」are basically the same word. Historically it is correct to write as 「向う (muka-u)」and we still use it but it is more common these days to use「向かう (muka-u)」avoiding confusion because we have another noun 「向こう (mukou)」meaning “over there” or “beyond” derived from a verb「向く (mu-ku)」meaning “to face” or “to turn toward”. 「向う」can be read both 「むかう (muka-u)」and「むこう (mukou)」 So 向-i and 向-kai are the same but I recommend you use 向-kai. The verb conjugations of 「向かう」and「向く」 are as bellow: 「向かう」（「向かい」as a noun ） 向かわない 向かいます 向かう 向かうとき 向かえば 向かえ 「向く」（「向こう」as a noun ) 向かない 向きます 向く 向くとき 向けば 向け It is confusing, isn't it?