The center of mass of a system of three particles of masses $1\, g,\, 2\, g$ and $3\, g$ is taken as the origin of a coordinate system. The position vector of a fourth particle of mass $4\, g$ such that the center of mass of the four particle system lies at the point $(1,2,3)$ is $\alpha(\hat{ i }+2 \hat{ j }+3 \hat{ k })$, where $\alpha$ is a constant. The value of $\alpha$ is