વેગમનના સરક્ષનના નિયમ અનુસાર 

હવે  $ \,\,\,_{{\upsilon _1}'}^ \to \, \cdot _{{\upsilon _1}'}^ \to =$ $( \,\,\,{\upsilon _1}'{\upsilon _2}'\,\,)^.(\,\,\,{\upsilon _1}'{\upsilon _2}'\,\,)$

$\therefore \,\,{\upsilon _1}^2 = \,\,\,_{{\upsilon _1}'}^ \to \, \cdot _{{\upsilon _1}'}^ \to  + _{{\upsilon _1}'}^ \to \, \cdot _{{\upsilon _2}'}^ \to  + _{{\upsilon _2}'}^ \to \, \cdot _{{\upsilon _1}'}^ \to  + _{{\upsilon _2}'}^ \to \, \cdot _{{\upsilon _2}'}^ \to \,\,\,\,\,\therefore \,\,\,{\upsilon _1}^2 = \,\,\,{\upsilon _1}^{'\,2} + 2_{{\upsilon _1}'}^ \to \, \cdot \,_{{\upsilon _1}'}^ \to  + {\upsilon _2}^{'\,2}\,\,\,\,\,\,\,…\,\,…\,\,…\,\,(1)$

પરંતુ ઉર્જા સરક્ષણ ના નિયમ પરથી  $\frac{1}{2}m{\upsilon _1}^2 + 0 = \frac{1}{2}m{\upsilon _1}^{'2} + \frac{1}{2}m{\upsilon _2}^{'2}\,\,\therefore {\upsilon _1}^2\, = \,{\upsilon _1}^{'2} + {\upsilon _2}^{'2}$

આ કિમંત સમીકરણ (1) માં મુક્તા  $,\,{\upsilon _1}^2\, = \,{\upsilon _1}^2 + 2_{{\upsilon _1}'}^ \to \, \cdot \,_{{\upsilon _2}'}^ \to \,\,\,\,$

$\,\,\therefore \,\,\,\,2_{{\upsilon _1}'}^ \to \, \cdot \,_{{\upsilon _2}'}^ \to \, = 0\,\,\,\,\therefore \,\,\,{\upsilon _1}'{\upsilon _2}'\,\,\cos \,\,\theta \, = \,0\,\,\,\therefore \,\,\,\,\cos \,\theta \, = \,0\,\,\,\therefore \,\,\,\theta \, = \,{90^ \circ }$