Let `overset rarr(r_(1)), overset rarr(r_(2))` be the position vectors of two particle of masses `m_(1)` and `m_(2)` situated at `A` and `B` respectively. Let the origin `O` of the frame of reference coincide with the centre of mass of the two particles.
`:. m_(1) overset rarr(r_(1)) + m_(2) overset rarr(r_(2)) = 0 or overset rarr(r_(1)) = - (m_(2))/(m_(1)) overset rarr(r_(2))`
or `|overset rarr(r_(1))| = (m_(2))/(m_(1)) |overset rarr(r_(2))| or (r_(1))/(r_(2)) = (m_(2))/(m_(1))`
Which was to be proved.
