If I have a vector location, as well as the rotator for the angle I want, how do I move the vector along that angle?

For example, if I have a vector that is at 10, -100, 5 and a rotator at 0, -63, 0, but I want him to shift to what would be the relative left by 150 units, how do I do that?

That’s simple, that is what the Get Forward Vector is for. You plug in a rotation (so basically an angle), and then it outputs a vector, then you multiply the return value by how many units along that angle you want, and then add the starting vector location. So here’s what you’d do according to your picture

Plug your blue into the rotation for Get Forward Vector, then multiply the output vector by 150, and then add the ‘Current Vector Location’, and then the result would be the ‘Desired Vector Rotation’.