Consider the function f(x, y) = (e - 3x) cos(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 (4,6) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 6i + 7j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 6). What is a? a=

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