6. Relative to a fixed origin \(O\), the points \(A\), \(B\) and \(C\) have coordinates ( \(2,1,9 ) , ( 5,2,7 )\) and \(( 4 , - 3,3 )\) respectively.
The line \(l\) passes through the points \(A\) and \(B\).
- Find a vector equation for the line \(l\).
- Find, in degrees, the acute angle between the line \(I\) and the line \(A C\).
The point \(D\) lies on the line \(l\) such that angle \(A C D\) is \(90 ^ { \circ }\)
- Find the coordinates of \(D\).
- Find the exact area of triangle \(A D C\), giving your answer as a fully simplified surd.