3. The rectangular hyperbola \(H\) has parametric equations $$x = 4 t , \quad y = \frac { 4 } { t } \quad t \neq 0$$ The points \(P\) and \(Q\) on this hyperbola have parameters \(t = \frac { 1 } { 4 }\) and \(t = 2\) respectively.
The line \(l\) passes through the origin \(O\) and is perpendicular to the line \(P Q\).

1. Find an equation for \(l\).
2. Find a cartesian equation for \(H\).
3. Find the exact coordinates of the two points where \(l\) intersects \(H\). Give your answers in their simplest form.