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