The plane $$\(\Pi_{1}\)$$ has vector equation $$\[ \mathbf{r}=\left(\begin{array}{l} 5 \\ 3 \\ 0 \end{array}\right)+s\left(\begin{array}{l} 3 \\ 0 \\ 1 \end{array}\right)+t\left(\begin{array}{r} 1 \\ -2 \\ 2 \end{array}\right) \]$$ where $$\(s\)$$ and $$\(t\)$$ are scalar parameters. The plane $$\(\Pi_{2}\)$$ has vector equation $$\(\mathbf{r} .\left(\begin{array}{r}5 \\ -2 \\ 3\end{array}\right)=1\)$$ (b) Determine a vector equation for the line of intersection of $$\(\Pi_{1}\)$$ and $$\(\Pi_{2}\)$$ Give your answer in the form $$\(\mathbf{r}=\mathbf{a}+\lambda \mathbf{b}\)$$, where $$\(\mathbf{a}\)$$ and $$\(\mathbf{b}\)$$ are constant vectors and $$\(\lambda\)$$ is a scalar parameter. (4)

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