5. The points \(A\) and \(B\) have coordinates \(( 3,4 , - 2 )\) and \(( - 2,0,7 )\) respectively. The equation of the plane \(\Pi\) is given by \(2 x + 3 y + 3 z = 27\).
- Show that the vector equation of the line \(A B\) may be expressed in the form
$$\mathbf { r } = ( 3 - 5 \lambda ) \mathbf { i } + ( 4 - 4 \lambda ) \mathbf { j } + ( - 2 + 9 \lambda ) \mathbf { k }$$
- Find the coordinates of the point of intersection of the line \(A B\) and the plane \(\Pi\).