PROBLEM SET 1: VECTOR ANALYSIS The vector area. [Problem 1.62, |Grifths] The integral 5 E [dd (4.1} s is sometimes called the vector area of the surface S . If S happens to he flar, then |E| is the ordinary scalar area, obviously. (a) Find the vector area of a hemispherical bowl of radius R.(4 pts) (13} Show that E = U for an}r closed surface. {4 pts) (c) Show that E is the same for all the surface sharing the same boundary. {4 pts) (d) Show that 1 . E: j*xdt, (4.2} 2 where the integral is around the boundaryr line. [4 pts) (e) Show that feast: 3x5, (4.3} for an]; constant vector E. {5 pts}. SHOW YOUR COMPLETE SOLUTION AND WRITE YOUR SOLUTION ON A PAPER