Question: Consider the function f ( x , y ) = ( e x - 3 x ) s i n ( y ) . Suppose

Consider the function f(x,y)=(ex-3x)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 (5,3) in the direction in which f decreases most rapidly.
vector =
(b) Suppose vec(v)=3vec(i)+3vec(j)+avec(k) is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (5,3). What is a?
a=

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