9 The plane \(\Pi _ { 1 }\) passes through the points \(( 1,2,1 )\) and \(( 5 , - 2,9 )\) and is parallel to the vector \(\mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k }\).
- Find the cartesian equation of \(\Pi _ { 1 }\).
The plane \(\Pi _ { 2 }\) contains the lines
$$\mathbf { r } = 2 \mathbf { i } - 3 \mathbf { j } + \mathbf { k } + \lambda ( \mathbf { i } - 2 \mathbf { j } - \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = 2 \mathbf { i } - 3 \mathbf { j } + \mathbf { k } + \mu ( 2 \mathbf { i } + 3 \mathbf { j } - \mathbf { k } ) .$$ - Find the cartesian equation of \(\Pi _ { 2 }\).
- Find the acute angle between \(\Pi _ { 1 }\) and \(\Pi _ { 2 }\).