find vector equation, algebra assignment help

quality work in a document.

1. Find the equation of the tangent plane at (2,3,1) to the surface x2 + y2 – xyz = 7. Do this 2 ways:
a) Viewing the surface as the level set of a function of 3 variables g(x, y, z).
b) Viewing the surface as the graph of a function of 2 variables f(x,y).
3. Consider the function f(x,y) = (e? – x) 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 (2, 3) in the direction
in which f decreases most rapidly.
b) Suppose = 51 +45 +ak is a vector in 3-space which is tangent to the surface S at the point P
lying on the surface above (2,3). What is a?