Determine $\beta $ and $\alpha $ by using vectors such that A, B and C lie in the same plane, given that vector $\overrightarrow{AB}=-4\overrightarrow{\u0131}-\overrightarrow{\u0237}-2\overrightarrow{k}$ and vector $\overrightarrow{BC}=4\overrightarrow{\u0131}+(\beta +3)\overrightarrow{\u0237}+(\alpha -6)\overrightarrow{k}$