1.6. CROSS PRODUCTS77and its signed area is12vextendsinglevextendsinglevextendsinglevextendsingle211−1vextendsinglevextendsinglevextendsinglevextendsingle=12[(2)(−1)−(1)(1)]=12[−2−1]=−32;you can verify from Figure1.38that the pathAmapsto→Bmapsto→Cmapsto→Atraversesthe triangleclockwise.-101234-10123456A(2,4)B(4,5)C(3,3)Figure 1.38: Oriented Triangle△ABC, Negative OrientationThese ideas can be extended to polygons in the plane: for example, aquadrilateral with verticesA,B,CandDis positively (resp. negatively)oriented if the vertices in this order are consecutive in the counterclockwise
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