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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