Let me start off by saying I am in no way familiar with vector math, so excuse me if I misuse the terminology. My goal is to find a point on a line that is directly orthogonal/perpendicular to another line/vector

I’m having trouble figuring out the math needed to do this. Basically if a have a vector, such as between the HumanoidRootPart of the character and some position, I need to find a vector that’s horizontally perpendicular in order to then find a point on that line.

I tried looking up possible solutions, however none gave me the desired results and I wasn’t able to understand why as my knowledge of vector math is very limited. Any help on how to find the orthogonal vector would be much appreciated!

Given one vector in three dimensions, there is an infinite number of perpendicular vectors to consider. However, based on the images you helpfully supplied, it looks like you can narrow this down to just one vector by taking the Cross product of your “RootPart-to-SomePosition” vector with the world up vector (0, 1, 0). Vector3 has a built-in method (Cross) that you can use for this:

local perpVector = someVector:Cross(Vector3.new(0, 1, 0))

Note that this perpendicular vector will not (necessarily) be unitary, so if you want to use it as a direction you may want to take the .unit of it after you do the Cross operation.