mathematics – Rotate relative to set point in a specified direction in a 3D space

I know there’s a geometry formula to calculate the next point in rotation relative to another point in 2D but I’m working in 3D and I want to calculate the next position in specified direction as well. Think Spiderman or the Bloodstalkers from ARK. I’m working in a game engine that uses the basic {x = 1, y = 2, z = 1} for vectors. I’m pretty bad at math so I honestly can’t figure this out myself.