Let α =3 i + j and β =2 i - j +3 k. If β = β_1- β_2, where β_1 is parallel to α and β_2 is perpendicular to α, then β_1 × β_2 is equal to:

Let $\displaystyle \vec{\alpha}=3 \hat{i}+\hat{j}$ and $\displaystyle \vec{\beta}=2 \hat{i}-\hat{j}+3 \hat{k}$. If $$\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2 \text {, where } \vec{\beta}_1 \text { is parallel to } \vec{\alpha} $$ and $\displaystyle \vec{\beta}_2$ is perpendicular to $\displaystyle \vec{\alpha}$, then $$\vec{\beta}_1 \times \vec{\beta}_2 \text { is equal to: } $$