Let C be a piecewise smooth, simple closed plane curve i
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Let C be a piecewise smooth, simple closed plane curve in R3 , which lies in a plane with unit normal NO D ai C bj C ck
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Let C be a piecewise smooth, simple closed plane curve in R3 , which lies in a plane with unit normal NO D ai C bj C ck and has orientation inherited from that of the plane. Show that the plane area enclosed by C is 1 2 I C .bz ? cy/ dx C .cx ? az/ dy C .ay ? bx/ dz:
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