2 The line \(l _ { 1 }\) has equation \(\mathbf { r } = \mathbf { i } + 3 \mathbf { j } - \mathbf { k } + \lambda ( \mathbf { i } - \mathbf { j } - 4 \mathbf { k } )\).
The plane \(\Pi\) contains \(l _ { 1 }\) and is parallel to the vector \(2 \mathbf { i } + 5 \mathbf { j } - 4 \mathbf { k }\).
- Find the equation of \(\Pi\), giving your answer in the form \(a x + b y + c z = d\).
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The line \(l _ { 2 }\) is parallel to the vector \(5 \mathbf { i } - 5 \mathbf { j } - 2 \mathbf { k }\). - Find the acute angle between \(l _ { 2 }\) and \(\Pi\).