The Integral is sometimes called the vector area of the surface S. If S happens to be flat, then |a| is the ordinay (scalar) area, obviously.

(a) Find the vector area of a hemispherical bowl of radius R.

(b) Show that a = 0 for any closed surface.

(c) Show that a is the same for all surfaces sharing the same boundary.

(d) Show that where the integral is around the boundary line.

(e) Show that for any constant vector c.

Transcribed Image Text:

da a Part (D) Pait (E) fie m. p(e r) dl = a x c.