Get further vector based on vector direction

Yes, but if A is not the origin it's not really more complicated. All you do is remove A, scale your relative vector and add A back on ^^. In general if you do B - A you get the relative vector from A to B. This you can scale as you want. The final result can simply be added back to A to get to point C.

 C = A + (B - A) * scale;

In distinct steps it's usually more readable, expecially with longer / meaningful variable names:

 Vector3 AB = B - A;
 C = A + AB * scale;

Note that if you want the resulting relative vector to have a certain length, you can normalize it before you scale it. That way the vector AB will have the exact length you specify.

 Vector3 AB = B - A;
 C = A + AB.normalized * newLength;

Always keep in mind that while code has to be readable / understandable by the compiler, it also should be readable and understandable by humans. The compiler doesn't care if you call your variable A, playerPosition or abz576eg5. A variable is just a variable. However you should write code that humans can understand easily. This is not only important when you work in a team where others might be watching or working on your code, but also for yourself. Try come back to more complicated code after a month, a year, ten years. If you have bad naming you will have a hard time to wrap your head around your own code.