Consider two points in 3D given by $A =(0,0,0)$ and $B=(b_x,b_y,b_z)$ given in cartesian form. $A$ is known and B is unknown.
Let's assume If I send a photon from $A$ towards $B$ along a straight line, it takes $x$ seconds for it to reach.
Now, consider I have a reflector at $C =(c_x,c_y,c_z)$.
$\vec{u}$ is the unit vector from A to C. Also, $\vec{v}$ is the unit vector from B to C. These unit vectors are known to me.
It is given that If I send the photon towards B, it will hit the reflector at $C$ and then reach point $B$ in $x+ 10$ seconds (In effect, it travels along 2 straight line segments AC and CB).
I am trying to compute the coordinates of the reflector, $C$, as well the point $B$ based on this information. Can someone help me with this.