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

$$x - 5 y - 2 z = 3$$ The plane \(\Pi _ { 2 }\) has equation $$\mathbf { r } = \mathbf { i } + 2 \mathbf { j } + \mathbf { k } + \lambda ( \mathbf { i } + 4 \mathbf { j } + 3 \mathbf { k } ) + \mu ( 2 \mathbf { i } - \mathbf { j } + \mathbf { k } )$$ where \(\lambda\) and \(\mu\) are scalar parameters.

1. Show that \(\Pi _ { 1 }\) is perpendicular to \(\Pi _ { 2 }\)
2. Find a cartesian equation for \(\Pi _ { 2 }\)
3. Find an equation for the line of intersection of \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\) giving your answer in the form \(( \mathbf { r } - \mathbf { a } ) \times \mathbf { b } = \mathbf { 0 }\), where \(\mathbf { a }\) and \(\mathbf { b }\) are constant vectors to be found.
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