# What's the point? 2

Geometry Level 4

A plane $$\color{#b7ae00}{\Pi }$$ has equation $\textbf{r}=\begin{pmatrix} 1 \\ 6 \\ 7 \end{pmatrix}+\lambda \begin{pmatrix} 2 \\ -1 \\ -1 \end{pmatrix}+\mu \begin{pmatrix} 2 \\ -3 \\ -5 \end{pmatrix}$ and the line $$\color{red}{l}$$ has equation $\textbf{r}=\begin{pmatrix} 7 \\ 4 \\ 1 \end{pmatrix}+t\begin{pmatrix} 3 \\ 0 \\ -1 \end{pmatrix}$ The point of intersection of $$\color{red}{l}$$ and $$\color{#b7ae00}{\Pi }$$ is $$P$$. If the coordinates of $$P$$ are $$(p, q, r)$$, find the value of $$pqr$$.

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