The lines $$\(l_{1}\)$$ and $$\(l_{2}\)$$ have equations $$\(\mathbf{r}=\mathbf{i}+3 \mathbf{j}-2 \mathbf{k}+\lambda(2 \mathbf{i}+\mathbf{j}+\mathbf{k})\)$$ and $$\(\mathbf{r}=\mathbf{i}-2 \mathbf{j}+9 \mathbf{k}+\mu(\mathbf{i}-4 \mathbf{j}+2 \mathbf{k})\)$$ respectively. The plane $$\(\Pi_{1}\)$$ contains $$\(l_{1}\)$$ and is parallel to $$\(l_{2}\)$$. Find the acute angle between $$\(\Pi_{1}\)$$ and $$\(\Pi_{2}\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . The point $$\(P\)$$ on $$\(l_{1}\)$$ and the point $$\(Q\)$$ on $$\(l_{2}\)$$ are such that $$\(P Q\)$$ is perpendicular to both $$\(l_{1}\)$$ and $$\(l_{2}\)$$.

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