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.
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.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.6: Equations Of Lines And Planes
Problem 2E
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