2 A surface has equation \(x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 2 z ^ { 2 } - 63 = 0\).
- Find a normal vector at the point \(( x , y , z )\) on the surface.
- Find the equation of the tangent plane to the surface at the point \(\mathrm { Q } ( 17,4,1 )\).
- The point \(( 17 + h , 4 + p , 1 - h )\), where \(h\) and \(p\) are small, is on the surface and is close to Q . Find an approximate expression for \(p\) in terms of \(h\).
- Show that there is no point on the surface where the normal line is parallel to the \(z\)-axis.
- Find the two values of \(k\) for which \(5 x - 6 y + 2 z = k\) is a tangent plane to the surface.