Vector Algebra: JEE Main 2021 Mathematics question

Let $\overrightarrow a$ = $\widehat i$ + 2$\widehat j$ $-$ 3$\widehat k$ and $\overrightarrow b = 2\widehat i$ $-$ 3$\widehat j$ + 5$\widehat k$. If $\overrightarrow r$ $\times$ $\overrightarrow a$ = $\overrightarrow b$ $\times$ $\overrightarrow r$, $\overrightarrow r$ . $\left( {\alpha \widehat i + 2\widehat j + \widehat k} \right)$ = 3 and $\overrightarrow r \,.\,\left( {2\widehat i + 5\widehat j - \alpha \widehat k} \right)$ = $-$1, $\alpha$ $\in$ R, then the value of $\alpha$ + ${\left| {\overrightarrow r } \right|^2}$ is equal to :