The direction (d) in which the target ball should move is
A is the center of the imaginary circle (where cue ball reaches next to target ball) and
B is the center of target ball.
Obviously d will not be equal to
AB.normalized if shot has an angle. i.e. if shot is done in a way that cue ball receives a clockwise rotation, then the target ball will receive a counter-clockwise rotation less than the rotation of cue ball as well as an additional force resulting from the torque of the cue ball.
The amount of rotation reduction and the additional force depend on physical attributes of the elements of the game. e.g. ball friction, pool friction, bounciness, etc..
If your game mechanics depend on Unity's Physics Engine then you probably will have a hard time estimating the exact value for these vectors. However if you go on writing your own physics engine (which is better in the end) you have to first write all your physics equations and integrate them into the visual representations shown in the picture to have the same visual and physical behavior.
I'm not a physics scientist so I don't know the equations you need. But you will certainly find them here.