2 A surface has equation $x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 2 z ^ { 2 } - 63 = 0$.\\
(i) Find a normal vector at the point $( x , y , z )$ on the surface.\\
(ii) Find the equation of the tangent plane to the surface at the point $\mathrm { Q } ( 17,4,1 )$.\\
(iii) 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 $h$.\\
(iv) Show that there is no point on the surface where the normal line is parallel to the $z$-axis.\\
(v) Find the two values of $k$ for which $5 x - 6 y + 2 z = k$ is a tangent plane to the surface.

\hfill \mbox{\textit{OCR MEI FP3  Q2}}