Yes, the line of relative motions necessarily the same after collision as before.
In accordance to the law of conservation of momentum, the total momentum of the particle having mass m₁ and the particle having mass m₂ before the collision equals their total momentum after the collision. The changes in momentum of the two objects have equal magnitudes and opposite signs, a necessary consequence of the law of conservation of momentum. Therefore the line of relative motions necessarily the same after collision as before.
In an elastic collision, the final velocity v_1f of the body having mass m₁ is,
v_1f = (m₁ – m₂/ m₁ + m₂) v_1i + (2m₂/ m₁ + m₂) v_2i
and the final velocity v_2f of the body having mass m₂ is,
v_2f = (2m₁/ m₁ + m₂) v_1i + (m₂ – m₁/ m₁ + m₂) v_2i
Here, v_1i is the initial velocity of the body having mass m1 and v_2i is the initial velocity of the body having mass m₂.
As the target particle (m₂) is at rest, thus, v_2i = 0.
Thus, v_1f = (m₁ – m₂/ m₁ + m₂) v_1i and v_2f = (2m₁/ m₁ + m₂) v_1i
Therefore the magnitude of the velocities of the bodies will depend upon the mass of the two bodies and initial velocities of the two bodies by the above two equations.
As, m₂ » m₁, thus,
v_1f ≈ - v_1i + 2 v_2i and v_2f = v_2i
When the massive particle is moving slowly or at rest, then
v_1f ≈ - v_1i and v_2f = 0
As, m₁ >> m₂, thus,
v_1f = v_1i and v_2f ≈ 2v_1i - v_2i
Therefore, as, m₂ >> m₁ or m₁ >> m₂, then the final velocity of the body will be equal to the initial velocity of the body.