Find a point on the surface where the tangent plane is perpendicular to the following tangent plane.

$\displaystyle

x^2+2y^2+3z^2=66

$

at the point(6,3,2)

so i got the gradient

<2x,4y,6z>

grad of(6,3,2)=<1,1,1>(<12,12,12>)

now how to go about finding a point on the surface where the tangent plane is perpendicular to the original plane?