Suppose that the pressure P and the temperature T at a point (x, y, z) are given by x2 + 2y2 P(x, y,2) = 1+ 22 (a) Suppose that the position of an airplane follows a path r(t) satisfying r(0) = ~j + k, r'(0) 2 2i Use the multivariable chain rule to compute the rate of change of pressure and temperature experienced by the airplane when t = 0. Then use this result to compute %(PT)2 along I'(t) when t = 0. Picking specific functions for r(t) will result in a grade of zero. The purpose of this question is to test your ability to use the multivariable chain rule in combination with other rules [mostly] symbolically. (b) What are all (unit) directions a bird at the point Q(0, 1, 1) should fly if it wants to keep both pressure and temperature constant? , T(x,y,z)=5+xyz 2