4 Points \(A , B\) and \(C\) have coordinates ( \(4,2,0\) ), ( \(1,5,3\) ) and ( \(1,4 , - 2\) ) respectively. The line \(l\) passes through \(A\) and \(B\).
- Find a cartesian equation for \(l\).
\(M\) is the point on \(l\) that is closest to \(C\). - Find the coordinates of \(M\).
- Find the exact area of the triangle \(A B C\).