Consider a relativistic elastic collision between two particles of equal mass, such as two protons. In the lab frame the target proton is at rest, and the incident proton has three-vector velocity \(v\). For nonrelativistic equal-mass collisions the two protons emerge at right angles to one another, except for the special case where one of the protons moves straight ahead while the other is at rest. Is that also true for relativistic collisions? Prove that it is or that it is not. Hint: Draw before-and-after pictures of the three-vector velocities for each proton in the \(\mathrm{CM}\) frame, and then transform to pictures in the lab frame.