Two spheres collide and assume that the collision is perfectly elastic. Also --only linear momentum. I have the relationship: (va' - vb') dot N = -(va - vb) dot N Where N is the normal vector at the point of collision. va and vb are initial velocities of object A and B, respectively. And va' and vb' are the final velocities of object A and B respectively. I want to know how this relationship is derived. This is what I try: Relative to object B, object A has velocity v_ab. Relative to object B, object B has velocity 0. m_a*v_a + m_b*v_b = m_a*v_a' + m_b*v_b' Relative to B: m_a*v_ab + 0= m_a*v_ab' + 0 v_ab = v_ab' That would give me this: (va' - vb') dot N = (va - vb) dot N But I am missing the negative sign, because they should be opposite. Please advise. Thanks in advance.