N2010 P1 Q10

The line \(l\) has equation \(\frac{x-10}{-3}=\frac{y+1}{6}=\frac{z+3}{9}\), and the plane \(p\) has equation \(x-2y-3z=0\).

1. Show that \(l\) is perpendicular to \(p\).[2]
2. Find the coordinates of the point of intersection of \(l\) and \(p\).[4]
3. Show that the point \(A\) with coordinates \((-2,23,33)\) lies on \(l\). Find the coordinates of the point \(B\) which is the mirror image of \(A\) in \(p\).[3]
4. Find the area of triangle \(OAB\), where \(O\) is the origin, giving your answer to the nearest whole number.[3]