Vector Algebra

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 :