Let L 1 and L 2 denote the lines r = i + (- i +2 j +2 k ), R and r = (2 i - j +2 k ), R…

Let L₁ and L₂ denote the lines
\(\vec{r}=\hat{i}+\lambda(-\hat{i}+2 \hat{j}+2 \hat{k}), \lambda \in R \text { and }\) \(\vec{r}=\mu(2 \hat{i}-\hat{j}+2 \hat{k}), \mu \in R\)
respectively. If L₃ is a line which is perpendicular to both L₁ and L₂ and cuts both of them, then which of the following options describe(s) L₃?