A unit vector perpendicular to the plane determined by the points $$P\left( {1, - 1,2} \right)Q\left( {2,0, - 1} \right)$$ and $$R\left( {0,2,1} \right)$$ is ............

Let $$\alpha ,\beta ,\gamma $$ be distinct real numbers. The points with position
vectors $$\alpha \widehat i + \beta \widehat j + \gamma \widehat k,\,\,\beta \widehat i + \gamma \widehat j + \alpha \widehat k,\,\,\gamma \widehat i + \alpha \widehat j + \beta \widehat k$$

Let $$\overrightarrow p $$ and $$\overrightarrow q $$ be the position vectors of $$P$$ and $$Q$$ respectively, with respect to $$O$$ and $$\left| {\overrightarrow p } \right| = p,\left| {\overrightarrow q } \right| = q.$$ The points $$R$$ and $$S$$ divide $$PQ$$ internally and externally in the ratio $$2:3$$ respectively. If $$OR$$ and $$OS$$ are perpendicular then

The vector $$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$ is