Let $$L_1$$ and $$L_2$$ denote the lines
$$\overrightarrow{r} = \widehat{i} + \lambda (-\widehat{i} + 2\widehat{j} + 2\widehat{k}), \lambda \in R$$ and
$$\overrightarrow{r} = \mu (2\widehat{i} - \widehat{j} + 2\widehat{k}), \mu \in R$$
respectively. If $$L_3$$ is a line which is perpendicular to both $$L_1$$ and $$L_2$$ and cuts both of them, then which of the following options describe(s) $$L_3$$?

$$\overrightarrow{r} = \frac{2}{9} (4\widehat{i} + \widehat{j} + \widehat{k}) + t(2\widehat{i} + 2\widehat{j} - \widehat{k}), t \in R$$

$$\overrightarrow{r} = \frac{2}{9} (2\widehat{i} - \widehat{j} + 2\widehat{k}) + t(2\widehat{i} + 2\widehat{j} - \widehat{k}), t \in R$$

$$\overrightarrow{r} = \frac{1}{3} (2\widehat{i} + \widehat{k}) + t(2\widehat{i} + 2\widehat{j} - \widehat{k}), t \in R$$

$$\overrightarrow{r} = t(2\widehat{i} + 2\widehat{j} - \widehat{k}), t \in R$$