Given surface is
Let be the position vector of any point P(x,y,z) of the required tangent plane and let be the position vector of the given point (1,2,2).
Therefore,=value of at point (1,2,2)=4i+2j+2k.
Hence the required equation of the tangent plane is
= or 2x+y+z=6\,</math>
Again,the required equation of normal is
which holds if the coefficients of i,j,k vanish simultaneously.
Hence from the above,the equations of the normal in cartesian form is