Science & Mathematics » Mathematics » Consider the function f(x,y)=(e^x-5x)sin(y).?

Consider the function f(x,y)=(e^x-5x)sin(y).?

Suppose S is the surface z=f(x,y).
(a) Find a vector which is perpendicular to the level curve of f through the point (2,6) in the direction in which f decreases most rapidly.

(b) Suppose v= 3i+2j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (2,6). What is a?

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