1. The line \(l _ { 1 }\) has equation

$$\mathbf { r } = \mathbf { i } + \mathbf { j } + \mathbf { k } + \lambda ( \mathbf { i } + 3 \mathbf { k } )$$ and the line \(l _ { 2 }\) has equation $$\mathrm { r } = 2 \mathbf { i } + s \mathbf { j } + \mu ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } )$$ where \(s\) is a constant and \(\lambda\) and \(\mu\) are scalar parameters.
Given that \(l _ { 1 }\) and \(l _ { 2 }\) both lie in a common plane \(\Pi _ { 1 }\)

1. show that an equation for \(\Pi _ { 1 }\) is \(3 x + y - z = 3\)
2. find the value of \(s\). The plane \(\Pi _ { 2 }\) has equation \(\mathbf { r } . ( \mathbf { i } + \mathbf { j } - 2 \mathbf { k } ) = 3\)
3. Find an equation for the line of intersection of \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\)
4. Find the acute angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) giving your answer in degrees to 3 significant figures.