Difference between 向かう, 向く, 向ける?

Question

From my understanding 向ける　is transitive and means to face/turn something towards something. > 安藤は日本国内から世界に目を向けたのです。 > > -Andou turned his eyes from inside Japan to the world. 向く　on the other hand is essentially just the intransitive form of 向ける, meaning to turn or face > 上を向いて > > -Look up Are my grammatical interpretations of 向ける　and 向く correct? and finally 向かう, which is also listed as intransitive. Does 向かう function in the exact same way as 向く？ Do their meanings overlap completely? If not what is the nuance that makes the two verbs different? In what cases would 向かう be used?

Answer 1

”向ける” is a transitive verb. -> 顔を窓に向ける。

”向かう” is an intransitive verb. -> 　大阪に向かう。大阪に、は直接目的格ではない。

”向く” is an intransitive verb. -> 海外へと向く心。上を向いて歩こう。

Answer 2

向かう is an intransitive verb meaning "to head for," such as 目的地に向かう (headding for the destination.) 向かう can also function almost like an adverb, and in this case, meaning "facing to" or "toward." For example, 観客に向かって、手を振る is to wave toward the audience.