Let C be a piecewise smooth, simple, closed plane curve in R³, which lies in a planewith unit normal N = ai + bj + ck and has orientation inherited from that of the plane.Prove that the plane area enclosed by C isS³ (bz - cy)dx + (cx − az)dy + (ay − bx)dz.-

Answered: Let C be a piecewise smooth, simple,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let C be a piecewise smooth, simple, closed plane curve in R³, which lies in a plane with unit normal N = ai + bj + ck and has orientation inherited from that of the plane. Prove that the plane area enclosed by C is (bzcy)dx + (cx - az)dy + (ay - bx)dz.