The centre of mass of system of three particles of masses 1g, 2g, and 3g is taken as the origin of a co-ordinate system. The position vector of a fourth particle of mass 4g. Such that the centre of mass of the four particle system lies at the point (1,2,3) is $\alpha \,{\rm{(}}\widehat {\rm{i}}{\rm{ + 2}}\widehat {\rm{j}}{\rm{ + 3}}\widehat {\rm{k}}{\rm{)}}$ Where $\alpha $ is a constant. The value of '$\alpha $' is