If the vectors \({\rm{\alpha \hat i}} + {\rm{\alpha \hat j}} + {\rm{\gamma \hat k}},{\rm{\;\hat i}} + {\rm{\hat k}}\) and \({\rm{\gamma \hat i}} + {\rm{\gamma \hat j}} + {\rm{\beta \hat k}}\) lie on a plane, where α, β and γ are distinct non-negative numbers, then γ is