Find a vector from this equation

Question

I have a directional vector $L_d$, that is the last direction that something has been moved. This vector is normalized. I also have the target point $T$ of this directional vector. The problem is, how do I find the origin $O$ of this movement? I.e. how to find $O$ from this equation: $L_d = \frac{T-O}{\|T-O\|_2}$

If this is even possible, I gladly accept every answer.

Answer 1

In short, you cannot: that equation is satisfied for all vectors in the form $O=T-\lambda L_d$ for some $\lambda>0$.