Q3. {a} The pressure p within a uid is given by the function prey) = e2 + twine-\"is\" using the directional derivative, find the rate of change of the pressure as we metre from the point {2, 3} in the direction a = ($1E :13?) _ [5 marks] {b} Find the mass of a solid 3 with density p = :r"2 + y? and S is bounded by the three coordinate planes and the plane 1: + 2;; + 3:: = 5. [5 marks] {c} For the following force field fr" and curve C calculate the work done W. # 2"!" 1 y t _ ET F{Iiy} Wiii'2+ygiaji C . r Lost1 y amt, [I i: t E E [5 marks] it'll Prove that (a) tV-ave-s v- _ = 2 ti: r 01\" an? swath {differentiable} vector field a and scalar field a. [5 marks] {e} The components of a velocity field are given by 152111 e =t calculate the streamline, the pathline and the streakline which passes through the point {1, 1) at t = 1. [Iii marks]