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

Your interpretation of 向く and 向ける seems fairly good. While the meaning of these three verbs tend to overlap they are not exactely the same, thus 向く and 向かう are not two verbs for a single concept.

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Now, let's delve into some details. As you noticed, 向く and 向かう are intransitive and 向ける is transivitive. It is often considered that 向く and 向ける form an intransitive/transitive pair whereas 向かう lives in its own world (which is not exactly true because those verbs are quite close).

• 向かう can express a movement in space, time or a change of situation:

  • 海へ向かう。 →　Go towards the sea.
  • 秋に向かう。　→　(lit. We're welcoming fall) Fall is coming.
  • 鏡{かがみ}に向かって、櫛{くし}で髪{かみ}を梳{と}かす。→　Comb one's hair in front of a (looking) glass.
  • 黎{れい}明｛めい｝に向かう。　→ 　The dawn is drawing near.
  • 平｛へい｝癒｛ゆ｝に向かう。　→　He/She is on his/her way to heal.

• 向ける can express a movement in space:

  • 星{せい}黎{れい}殿{でん}に足を向ける　→　(lit. direct one's feet towards the palace of the black star)
    Walk towards the palace of the black star.
  • 扇子を顔に向ける。　→　Direct the fan towards one's face.

• 向く shows that something faces a direction.

  • 上を向いてください。　→　Look up.
  • 扇子を顔に向く。　→　Direct the fan towards one's face. (@HiruneDiver mentioned that since 向く is the literary version of 向ける it can be used here. But usually 向ける would be better. see comments)

Nevertheless, it should be noted that those verbs have other meanings as well.

1. 将軍を向ける。→　Send a general (for some kind of mission)
   (Here 向ける means `send somebody for a task')
2. その教科書は初心者に向いています。→　This textbook is addressed at beginners.
3. 頼もしい方に向いた任務。→　A work for/addressed at somebody reliable.
4. etc。 (each letter hide a link)

Usage 2. and 3. are well-known through the two suffixes 向き and 向け.

• 初心者向きの教科書。→ A textbook good for beginners. (It suits them).　
• 初心者向けの教科書。→ A textbook addressed at beginners. (It had been designed with beginners in mind).

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Last thing that is worth mentioning is, that while 向く is not a verb of motion (unlike 飛ぶ,歩く,走る,…) it takes the を particle very often (に is also possible). Some other verbs behave like this, for example, 振り向く and 振り返る. More information on this subject can be found here.