Consider the surface given by S: 7xy + 2yz - 7zx = 0. (a) Differentiating implicitly the equation of the surface, the partial derivatives oz and az can be expressed as ay Ay + Bz 7x + Cy and az Ax - Cz ay 7x + Cy where A = B = C = P7 , g, 1) and write it in the box below. (b) Compute the normal vector u to tie surface S at the point P(1 u : 5i 1 (Enter your vector in the form ) (0) Professor Jeya tells you that the normal v to the surface defined by the equation F(:1:, y, z) : 0 at the point P(1, %, 1) is v : (7, O, 2). Explain briefly whyr the tangent planes at the point of intersection P(1, %, 1) of the surfaces 73y + 2yz 73:}: = 0 and F[a:,y, z) = 0 are perpendicular. 3C [a l' l Q a' E 0 E3323\" Av e- 1; B I u s xa xa O O Styles ' Font ' Size ' Words: 0 A