Consider the surface 1 x2 + 16 y2 + 16 z2 = 33 and the point P = ( 1, 1, 1 ) on this surface.

a) The outward unit normal at the point P is ??? I + ??? J + ??? K. b) The equation of the tangent plane at the point P is
z = ??? x + ??? y + ??? .

Question

Consider the surface 1 x2 + 16 y2 + 16 z2 = 33 and the point P = ( 1, 1, 1 ) on this surface.

a) The outward unit normal at the point P is  ??? I + ??? J + ??? K. b) The equation of the tangent plane at the point P is 
z =  ??? x + ??? y + ??? .

amistre64 · Answer

the gradient of the equation gives you the equations for the normal vector parts

amistre64 · Answer

the equation of the tangent plane is of course, the normal applied to the given point

amistre64 · Answer

Dx = 2x Dy = 32y Dz = 32z at 1,1,1 = <2,32,32>; or reduced to: <1,16,16>

amistre64 · Answer

your surface resembles and ellipsoid if im not mistaken