Vector product of two vectors $2\hat i\, + \,\hat j\,$ and $\hat i\, + \,2\hat j\,$ is

Consider three vectors $A =\hat{ i }+\hat{ j }-2 \hat{ k }, B =\hat{ i }-\hat{ j }+\hat{ k }$ and $C =2 \hat{ i }-3 \hat{ j }+4 \hat{ k }$. A vector $X$ of the form $\alpha A +\beta B$ ( $\alpha$ and $\beta$ are numbers) is perpendicular to $C$.The ratio of $\alpha$ and $\beta$ is

A vector $\vec{A}$ points towards North and vector $\vec{B}$ points upwards then $\vec{A} \times \vec{B}$ points towards ...........