- The line \(l\) has equation
$$\frac { x + 2 } { 1 } = \frac { y - 5 } { - 1 } = \frac { z - 4 } { - 3 }$$
The plane \(\Pi\) has equation
$$\mathbf { r } . ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } ) = - 7$$
Determine whether the line \(l\) intersects \(\Pi\) at a single point, or lies in \(\Pi\), or is parallel to \(\Pi\) without intersecting it.
(5)