The centre of mass of a system of three particles of masses $1g$ , $2g$ and $3g$ is taken as the origin of a coordinate 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 $\left(1,2,3\right)$ is $\alpha \left(i^{\wedge }+2j^{\wedge }+k^{\wedge }\right),$ where $\alpha$ is a constant. The value of $\alpha$ is :-