Consider the function f(x,y)=(e^x−2x)sin(y). Suppose S is the surface z=f(x,y).

Question

(a) Find a vector which is perpendicular to the level curve of ff through the point (3,3)(3,3) in the direction in which ff decreases most rapidly.

vector = <-(e^3-2)sin(3), -cos(3)(e^3-6)> (My answer which was correct)

Suppose v⃗ =3i⃗ +1j⃗ +ak⃗ v→=3i→+1j→+ak→ is a vector in 3-space which is tangent to the surface SS at the point PP lying on the surface above (3,3)(3,3). What is aa?

a=

i got 3[e^3-1]sin(3)+cos(3)(e^3-6)

and i keep getting it wrong when solving

Answer 1