Both prepositions are correct but have different meanings: “The VP is responsible to the president for carrying out the plan.” This means that the VP is supposed to carry out the plan, and that the VP must answer to the president (regarding the execution of the plan).

Hi there, native speaker here - we don’t say responsible of, or responsible to in any circumstances. We can say someone’s responsibility is to (verb). I’ll give you some examples of how I commonly see this used. Elena is responsible for her students safety. It Is Elena’s responsibility to keep her students safe. Or if you want to hear a singular example, it’s similar. Elena is responsible for John’s safety. It Is Elena’s responsibility to keep John safe. Or, examples you may hear in the workplace: Elena is responsible for sending out customer communications. It is Elena’s responsibility to ensure her team is performing well.

Whether you are talking about a thing or a person or an action, it is always ‘for’. I am responsible for the bathroom, so I clean it every Saturday. I am responsible for my younger cousins when we go to the park. I am responsible for keeping the goat out of the flower beds. Does that make sense?