に向かって/に向けて

「に向かって」
1. Indicates the direction (N2) toward which the subject N1 is facing when performing action V. V expresses a change in posture or movement at the spot of N1, such as sitting, standing, lying down, etc.
2. Indicates the destination (N2) toward which the subject N1 is moving or heading. V is an action expressing movement, such as walking, progressing, etc. N2 is not limited to physical locations; it can also be an object (like a wall, a door) or an abstract destination (the future, a dream).
3. Indicates that N2 is the target receiving the action V of the subject N1.
- When N2 is a person, V is an action impacting the person, such as talking to, addressing, greeting, smiling at, etc.
- When N2 is an object, it not only shows the direction N1 is facing (in space) but also implies that N1 sees N2 as a tool to perform V.
Example: 小林さんは鏡に向かって化粧する。Kobayashi applies makeup facing the mirror, meaning using the mirror as a tool to apply makeup.

「に向けて」
1. Indicates the direction (N2) to which the subject N1 causes N to face when performing action V. V (being a transitive verb) impacts N in place.
2. Indicates the destination (N2) toward which the subject N1 is moving. V is an action expressing movement, such as departing, etc. N2 can only be a physical location.
3. Indicates that N2 is the recipient of N from the subject N1. N can be an object, attitude, or words, information that N1 intentionally conveys to N2.
4. Indicates the goal (N2) that the subject N1 wants to realize or prepare for.