Vector Algebra

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