1. The plane \(\Pi _ { 1 }\) has equation

$$\mathbf { r } = 2 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } + \lambda ( \mathbf { i } + 2 \mathbf { j } - 3 \mathbf { k } ) + \mu ( - \mathbf { i } + 2 \mathbf { j } + \mathbf { k } )$$ where \(\lambda\) and \(\mu\) are scalar parameters.

1. Find a Cartesian equation for \(\Pi _ { 1 }\) The line \(l\) has equation $$\frac { x - 1 } { 5 } = \frac { y - 3 } { - 3 } = \frac { z + 2 } { 4 }$$
2. Find the coordinates of the point of intersection of \(l\) with \(\Pi _ { 1 }\) The plane \(\Pi _ { 2 }\) has equation $$\mathbf { r . } ( 2 \mathbf { i } - \mathbf { j } + 3 \mathbf { k } ) = 5$$
3. Find, to the nearest degree, the acute angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\)