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LingakuLingaku[noun] + に向かって [noun] + に向けて
に向かって means "towards", "facing": movement in the direction of a place, or an action aimed at someone in front of you. にむけて向けて means "for", "aimed at": work towards a goal, an event or an audience. Both go straight after a noun.
The two come from a pair of verbs. むかう向かう is intransitive: you head somewhere, or face something. むける向ける is transitive: you point something at a target. So に向かって is about where you are going or facing, and に向けて about what you are preparing for – an exam, an event, a date.
With a physical target, に向けて keeps its own object with を: you point something at it.
A goal like ゆめ夢 or もくひょう目標 takes either. に向かって pictures you moving towards it, which is why ゆめ夢にむかって向かってがんばる頑張る is a set phrase.
These go beyond direction and goals.
に向かって with a person is talking to their face. With someone older or senior it often carries a rebuke: how dare you say that to them.
に向かって also works with a season or a condition the situation is moving towards.