The balls in this display are of equal mass. The initial velocities were chosen to give a glancing collision rather than head on. The line of sight is the thin gray line and the component of each ball's velocity in the line of sight is the green vector. Notice after the collision, the line of sight vectors reverse direction as you would expect from balls of equal mass and equal initial velocity.
We halt the model immediately after the collision and for the red ball, display its velocity vector just before and just after the hit. The cyan vector is the vector difference between the before and after hit velocities in the line of sight. You can see that the post hit velocity vector is the vector sum of the pre-hit velocity vector and this change in line of sight velocity.