Do I have negative orbital vector and if so, what's the best way to go ahead for a permanent solution? (Photos)

Yes you do and the best treatment is likely permanent infraorbital rim silicone implant but need personal evaluation to determine accurately.

At home peels like cosmelan, enlighten and aerify along with dermarolling (MTS roller with anteage MD ampules) should be started now. There are many things you can do to treat under eye hollows and dark circles. A surgical option to remove skin and/or fat will such as lower eyelid blepharoplasty with or without fat pad repositioning will be the best long term. There are many things you can do to treat under eye hollows and dark circles without surgery. Non invasive less downtime options such as fillers (Belotero, Juvederm Volbella​), lasers (Moxi/Halo/Fraxel/CO2​), Renuvion (J-Plasma), microneedling/PRP, stem cells and microneedling RF like Fractora PiXel8 or Morpheus can all help give some improvement. Accutite can often be used or stronger lasers like erbium or co2 spot treatment can tighten the skin and give very quick improvement in wrinkles and texture. A surgical option to remove skin and/or fat might be the best solution long-term. I suggest you get a formal consultation to see what is best for you and your goals. Best, Dr. Emer.

It would help to have photographs taken with better lighting, but it appears that you would do well having a lower blepharoplasty. This is a hereditary condition that is easily remedied with a very simple and safe surgical procedure.