7. The line \(l _ { 1 }\) has equation
$$\frac { x - 3 } { 4 } = \frac { y - 5 } { - 2 } = \frac { z - 4 } { 7 }$$
The plane \(\Pi\) has equation
$$2 x + 4 y - z = 1$$
The line \(l _ { 1 }\) intersects the plane \(\Pi\) at the point \(P\)
- Determine the coordinates of \(P\)
The acute angle between \(l _ { 1 }\) and \(\Pi\) is \(\theta\) degrees.
- Determine, to one decimal place, the value of \(\theta\)
The line \(l _ { 2 }\) lies in \(\Pi\) and passes through \(P\)
Given that the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\) is also \(\theta\) degrees, - determine a vector equation for \(l _ { 2 }\)