1) For the following two Cartesian vectors, answer the questions below. ???? = ???? 2???????????? 3 ???????? 2 ???? ???? = ???? 2????????????+ 14????????

a. Determine the quantity ???? ????

b. Find ????????. Note that the ax terminology refers only to the x component of a.

c. Find ????. d. Determine the curl of ????

2) The ideal gas law states that temperature is related to pressure and density in the following way: ???? = ???????????????? Here, p is pressure in Pa, T is temperature in K, and is density in kg/m3 . The term Rd is a gas constant for dry air (287 J/kg K). Assuming the field from (2) is an isothermal 300K pressure field, determine the density gradient at Darth Vaders position ????.