Suppose you have a collection of particles, all moving in the x direction, with energies ${\mathbf{E}}_{\mathbf{1}}\mathbf{,}{\mathbf{E}}_{\mathbf{2}}\mathbf{,}{\mathbf{E}}_{\mathbf{3}\mathbf{,}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}}$. and momenta${\mathbf{p}}_{\mathbf{1}}\mathbf{,}{\mathbf{p}}_{\mathbf{2}}\mathbf{,}{\mathbf{p}}_{\mathbf{3}\mathbf{,}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}}$ . Find the velocity of the center of momentum frame, in which the total momentum is zero.

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