12. The line \(l _ { 1 }\) has Cartesian equation
$$x - 2 = \frac { y - 3 } { 2 } = z + 4$$
The line \(l _ { 2 }\) has Cartesian equation
$$\frac { x } { 5 } = \frac { z + 3 } { 2 } , \quad y = 9$$
Given that \(l _ { 1 }\) and \(l _ { 2 }\) meet at the point C , find
- the coordinates of C .
The point \(\mathrm { A } ( 2,3 , - 4 )\) is on the line \(l _ { 1 }\) and the point \(\mathrm { B } ( - 5,9 , - 5 )\) is on the line \(l _ { 2 }\).
- find the area of the triangle \(A B C\).