2 The points \(\mathrm { A } , \mathrm { B }\) and C have coordinates \(( 1,3 , - 2 ) , ( - 1,2 , - 3 )\) and \(( 0 , - 8,1 )\) respectively.

1. Find the vectors \(\overrightarrow { \mathrm { AB } }\) and \(\overrightarrow { \mathrm { AC } }\).
2. Show that the vector \(2 \mathbf { i } - \mathbf { j } - 3 \mathbf { k }\) is perpendicular to the plane ABC . Hence find the equation of the plane ABC .
3. Write down normal vectors to the planes \(2 x - y + z = 2\) and \(x - z = 1\). Hence find the acute angle between the planes.
4. Write down a vector equation of the line through \(( 2,0,1 )\) perpendicular to the plane \(2 x - y + z = 2\). Find the point of intersection of this line with the plane.
5. Find the cartesian equation of the plane through the point \(( 2 , - 1,4 )\) with normal vector $$\mathbf { n } = \left( \begin{array} { l } 1
   1
   2 \end{array} \right) .$$
6. Find the coordinates of the point of intersection of this plane and the straight line with equation $$\mathbf { r } = \left( \begin{array} { r } 7
   12
   9 \end{array} \right) + \lambda \left( \begin{array} { l } 1