Question: 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,

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.

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

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

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